Introductory supersymmetry literature for the perplexed


Supersymmetry (SUSY) has been around in particle physics literature for over 30 years. It’s one of a theorist’s main tools for model building at the TeV scale, but is also a necessary ingredient for superstring theories, a rich playground for nonperturbative physics, and is [apparently] independently useful in mathematics.

So — how does one go about learning supersymmetry? Here are my humble thoughts, with the understanding that a literature review by someone who’s recently learned SUSY will be more useful to beginners than one by a senior faculty member who has lost touch with what it’s like to approach a new subject tabula rasa.

I will assume that one is interested in SUSY from a particle phenomenology perspective, since that’s my own background. The point, of course, is that the more SUSY you know the easier it is to learn more. Initially all of the literature is all unintelligible, but once you’ve worked through one presentation, the rest will fall into place readily. The key is to start in the right place. Here I’ll give a biased review of the literature available for a first-time SUSY-learner. I give some suggestions for where to find pedagogical beyond-introductory reading is provided at the end.

Prerequisites: what you should already know

(1) Quantum field theory. You should be comfortable reading a Lagrangian and writing down Feynman rules, working with [Dirac] spinors, (anti-)commutation relations, path integrals, and all that. It helps if you have a handle on Grassman variables (e.g. in the fermionic path integral) and have some working knowledge of renormalisation. If you’re familiar with BRST symmetry, you’ve already seen a kind of SUSY. I would say having worked through Peskin chapters 1-5, 9 (and ideally 10,12), and 15-16 would be a necessity. Alternately, the Ryder’s text up to chapter 8—but just enough of each chapter to feel comfortable reading the next chapter. If you’re looking for an approach with fewer physical pages to read, you could probably get away with Zee I, II, IV.1, IV.5, IV.6. For more options, see this post.

(2) Representation theory. This is what trips up a lot of young theorists these days: the lack of a proper representation theory (for physicists) course before taking quantum field theory. It’s nice to know about reps of SU(N) and how to draw weight diagrams, but what you really need is to understand the representations of the Poincare group. I.e. to really understand what a spinor is. This is especially important in SUSY because you’ll be playing with two-component spinors and funny indices that you might not be used to from conventional QFT. Unfortunately there don’t seem to be many good treatments of this. You’ll need to understand: what is meant by the (1/2,0) and (0,1/2) spinor reps of the Poincare group, the difference between a dotted and undotted index, the index structure of the sigma/gamma matrices, how these things behave under a Lorentz transformation. The best I’ve found are Dr. Gutowski’s notes for his Part III Symmetries and Particle Physics course. (These seem to disappear at the beginning of the year and gradually reappear as the course is lectured.) Another treatment I’ve found recently is chapter 3 of Elementary Particle Theory by Martin and Spearman. Alternatives are chapters 2.3-2.5 of Weinberg Vol I chapter 2.3-2.5, Bailin and Love Supersymmetric Gauge Field Theory and String Theory chapter 1.2, or appendix A of Wess and Bagger Supersymmetry and Supergravity. Chapter 11.2 of Ryder’s Quantum Field Theory may also provide some explicit steps if you’re feeling unsure of yourself.

(3) Standard Model. In some sense this is the combination of (1) and (2) above. You should have a good feel for how the Standard Model works: its particle content, interactions, representations, etc. It helps if you can write down the Standard Model lagrangian off the top of your head, but at a minimum you should recognise all the terms. The best book on this I’ve found is Burgess and Moore. It’s not terribly technical, but contains all the insight you’ll need to understand the Minimally Supersymmetric Standard Model. (You can skip any chapter about particular processes.) Howard Georgi’s Weak Interactions book is also a fantastic resource for the more technically-inclined.

(4) `Pop-SUSY’. You should have a conceptual understanding of supersymmetry at a popular level. It can feel like SUSY requries a lot of formalism, so it helps if you know what the end-point of it all. Based on reading Scientific American-esque magazines or blogs, you should have a hand-wavy picture of supersymmetry and why it’s important. If you can recite the MSSM particle content and say a word or two about what’s interesting about it, then you’re on the right track.

Absolute Beginners

For those who have never seen superfields before, SUSY can be an absolutely daunting thing. When I first approached SUSY from an independent-study prespective, I found Martin Nilsson’s MSc thesis rather helpful. However, as usual, the absolute best option is to study with a group of intelligent friends and discuss with one another. The second best option is to attend a lecture and be able to ask questions of the lecturer.

A road map to learning SUSY

It might help to start with roadmap, since at some point you might start wondering what these dotted indices have to do with anything. Here’s what a `typical’ introductory curriculum looks like:

(Caution: I’ll recommend a few references for each topic, please be aware that each text uses its own metric and spinor conventions!)

  1. Background: Motivation: you’ll bump into words like Coleman-Mandula, hierarchy problem, dark matter, grand unification… you don’t need to know anything about these things before-hand. Two-compoenent spinors, however, are very important. Since supersymmetry relates bosons and fermions, you should start by becoming very familiar with spiniors. In SUSY we typically work with two-component Weyl spinors, which requires one to be precise about notions of chirality/helicity and charge/parity conjugation. Reading: see (2) and (4) above. For motivation, my favourite presentation is the first few sections of Prof. Murayama’s ICTP lectures, see in particular the analogy to positrons. The standard phenomenological motivations are listed at the beginning of Prof. Martin’s review. If inclined, you could read about supersymmetric quantum mechanics in, e.g. Binetruy’s book or Prof. Argyres’ notes… but I found that when I was first learning SUSY this confused me more than it helped.
  2. SUSY algebra: The first step to supersymmetry is understanding the SUSY algebra, an extension of the Poincare algebra. You should already be familiar with how quantum fields transform as representations of the Poincare algebra. Supersymmetry extends the Poincare group into the super-Poincare group which includes spinorial generators (makes sense if you’re relating fermions with bosons, right?), and so you’ll work out the (anti-)commutation relations of this extended algebra to understand the particle reps that come out. You can ignore extended supersymmetry if you’re already feeling inundated with indices. I’ve personally think Bailin and Love have the right presentation for a first go, while Wess and Bagger is a bit more useful as a reference. For a few more words see chapter 3 of Drees et al., Theory and Phenomenology of Sparticles. For a lot more words, all of them meaningful but perhaps too much for a beginner, see chapter 25 of Weinberg vol 3.
  3. Superspace: Now that you’re happy with SUSY representations, you’ll want to build supersymmetric lagrangians. You could do this right now, with some fiddling of auxilliary fields that come out of nowhere (this is what Martin does in his review). However, a proper theorist should be familiar with the much more elegant superspace formalism where define a lagrangian density over Minkowski space extended with Grassmanian directions. Yes, this is weird. The point is that we can write an entire SUSY representation as a superfield and write your lagrangian in terms of these objects. (Sanity check: this is exactly what we do with the Poincare group: you don’t write a Dirac spinor as four separate fields with the same couplings.) When you integrate out the Grassmanian directions, you’re left with a `usual’ lagrangian density with a mess of scalar/spinor/vector fields that happens (by construction) to be invariant under supersymmetry. Once again I suggest Bailin and Love for this. With the exception of Martin, all of the other comprehensive reviews explain superspace with slightly different flavour but nearly the same content. The now-online Superspace text and Weinberg Vol 3 chapter 26 hav a bit more embellishment, but I think those are best left for after one has mastered the bare-bones structure of SUSY.
  4. Supergraphs: Supergraphs are a method of drawing Feynman diagrams of superfields. I haven’t gotten around to studying these properly and they don’t seem to be emphasised in the modern reviews. You can find out more about them in Wess and Bagger, Weinberg Vol 3 chapter 30, or Gates’ et al. in Superspace. I suspect that you can get away with studying supergraphs much later, or perhaps never-at-all if you’re really phenomenological.
  5. Irreducible superfields: Once you’re happy with the superspace formalism, the next step is to define irreducible superfields. The two that you’ll get used to are the chiral and vector superfields, which will end up giving you the SUSY generalisations of your standard model fermions and gauge bosons respectively. By the end of all this you should be happy with the Wess-Zumino model, the basics of supersymmetric QED, and the basics of the generalisation to non-Abelian groups. You should be familiar with words like superpotential, Kahler potential, (super)covariant derivative, etc. Once again Bailin and Love is my first choice here, while Wess and Bagger have some very useful insights (if at times cryptically terse). Dress et al. goes into some nice detail about SQED. The text Weak Scale Supersymmetry by Baer and Tata have a nice discussion of superfields and SUSY gauge theories in chapters 5-6, but the cost is having to adjust to 4-component spinor notation. Appendix C of Binetruy’s new Supersymmetry text has the usual treatment with a table of common conventions at the end, which might be worth sticking on your wall if you’re bouncing between texts.

At this point you’ve pretty much `learned’ supersymmetry, in the same sense that you could say you’ve `learned’ QFT after studying Yang-Mills theory. But, just as everyone learns at least a bit of the Standard Model, it behooves you to learn the minimally supersymmetric standard model (MSSM) since you’ve already done all the heavy-lifting. After this, you can go on to fancier things beyond my current domain of familiarity. (I can only provide suggestions for topics I’m familiar with, unfortunately.)

  • The MSSM and SUSY breaking: To first order, the MSSM is what you trivially get by promoting the Standard Model fields to the appropriate superfields. There are some subtleties: determining the `appropriate’ superfield irrep, holomorphy of the superpotential and cancellation of the chiral anomaly requires two Higgs doublets, and R-parity as a hack for troublesome processes. However, there is one big lesson for phenomenologists: breaking the MSSM. You should understand why the general soft-SUSY-breaking terms look the way they do, and figure out what effect they have on the low-energy physics. For this section, I think Prof. Martin’s review is the best reference (despite not using superfields) for its comprehensive discussion of SUSY breaking. More discussion is available in the two recent phenomenologically-oriented books, Sparticles (Dress et al.) and Weak Scale SUSY (Baer and Tata). For a slightly more formal approach, Weinberg vol 3 chapter 28 is very good.
  • SUSY breaking models: While one can write down general low-energy SUSY breaking terms for the MSSM, the particular high-scale mechanism by which supersymmetry is broken is unknown. The for the traditional approaches, I suggest Baer and Tata chapter 11, Dress et al. chapter 12-13, and Prof. Martin’s review. More advanced breaking comes from SUSY dynamics, see Terning’s Modern Supersymmetry and Binetruy’s Supersymmetry. Profs. Intriligator and Seiberg have also put together a nice review based on recent lectures on dynamical and metastable SUSY breaking. Shadmi and Shirman have a more detailed review of dynamical SUSY breaking.
  • SUSY model-building and formal things: There’s a lot one can do with SUSY model building. On the more phenomenological side, this involves affixing letters infront of the MSSM (nMSSM, cMSSM, …). On the more formal side, one can look at SUSY-breaking in stringy models, BPS states, supergravity and a bunch of other things that are outside of my current domain of familiarity. I’ll make a few recommendations for literature that has caught my attention, but keep in mind that I haven’t yet had a chance to go into much detail into any of them. For a broad overview, Dine’s Supersymmetry and String Theory is very readable and full of insight about the standard model, SUSY, and string theory. Mohapatra’s Unification and Supersymmetry is another work that touches on many topics in general “beyond the standard model” model building. Both of these books shouldn’t be thought of as textbooks in a conventional sense, but rather interfaces between a proper textbook/pedagogical review article and research. The books treat many topics rather briefly (leaving most calculations to the reader), but are able to tie them all together so that you can pick up a lot of physical intuition along the way. I think Terning’s Modern Supersymmetry: Dynamics and Duality is the current standard for more advanced formal topics. (At least my `token’ string theory friend Chris seemed to like it.) A more beginner-friendly review along these lines are Professor Lykken’s TASI lectures. Another recent text of broad interest is Binetruy’s Supersymmetry. Like the previous books, I wouldn’t necessarily recommend it as a first book (but the appendices are quite useful for a beginner!), but it does approach several topics from a model-builder’s point of view. It’s also one of the few books to mention SUSY in cosmology. And here’s a review of SUSY GUTs.
  • SUSY Collider Phenomenology: For nose-to-the-grindstone phenomenologists, the three resources I’m familiar with are Prof. Martin’s review, and the aforementioned books by Drees et al. and Baer/Tata.
  • Supergravity: Wess and Bagger seems to be the main choice here. I believe Weinberg vol I mentions some generics about spin-3/2 fields, while the Feynman Lectures on Gravitation might be a nice thing to read on-the-side for its treatment of gravity as a quantum field. There is an older SUSY/SUGRA text by West, but I never really got around to going through it properly. Weinberg vol 3 chapter 31 also includes a treatment of gravity within supersymmetry. Most of the other modern texts mention something about supergravity, though not necessarily giving the detail one would wish for a dedicated study. I think the current state of the literature is that a lot of the tedious calculations are left to the reader to flesh out. I should note that Bailin and Love have quite a bit on supergravity… but I never got that far in the text, perhaps because they supergravity chapter sits right where I would expect a chapter on the MSSM.šŸ™‚
  • Fancy Stuff: As is the case with his other two volumes, one can find a wealth of fancy topics in Weinberg’s volume 3. (Or perhaps I’ve twisted my definition such that anything in this volume is defined to be `fancy’?) Here you’ll find a discussion of the Coleman-Mandula theorem, non-renormalisation theorems, extended supersymmetry and monopoles (a very interesting subject!), supergraphs, SUSY in higher dimensions, etc.
  • Mathsy: Mars recently asked me for recommendations for introductory SUSY literature for a mathematician (I recommended Prof. Argyres’ notes.) though I haven’t quite figured out why SUSY is interesting to mathematicians. Apparently they’re relevant for something with index theorems (see the relevant chapter in Nakahara’s Geometry, Topology and Physics… which you should already have on your bookshelf for reference and pleasure reading!). Professor O’Farrill’s research page has a description about his mathsy interest in SUSY. I’ve been told that Varadarajan’s Supersymmetry for Mathematicians is of general interest to those who preferred to learn about Lagrangians from Arnold’s Mathematical Methods of Classical Mechanics.

Literature List

Here is a semi-comprehensive list of literature that I’m not necessarily famliar with, but that I think might be useful to others. First up are what I would consider the canonical texts for beginners.

  1. Stephen Martin, A SUSY Primer. Since its first edition, this continuously-updated paper has gotten a lot bigger. In many respects, this is one of its main strengths: the author isn’t afraid to use plenty of words to describe something when he feels that plenty of words is necessary. For a beginner, it can feel a little bit chatty if you’re eager to cut to the chase. However, this remains one of the most recommended pieces of introductory literature on the subject. The discussion is full of great statements about the MSSM, SUSY-breaking, and collider signatures. My personal reservation is that it doesn’t use superfields. On the one hand it is very helpful to see things from an orthogonal approach and you don’t have to learn a new formalism—you’re just using the quantum field theory that you’re familiar with from Peskin and Schroeder. On the other hand, I really think every student of SUSY should be raised on superfields. … unless you’re an experimentalist, in which case this review, with its balance of down-to-earth phenomenology, might be just what you’re looking for.
  2. Bailin and Love, Supersymmetric Gauge Field Theory and String Theory. This is probably the standard textbook to pick up at a bookstore. It’s roughly in the order of topics in which I learned the subject, so I like it quite a bit. Unfortunately they sacrifice an introduction to the MSSM in favour of jumping into supergravity, so you’ll have to go elsewhere for that. (It’s because of this that I never got around to going back to Bailin and Love to read their supergravity chapters!) I have no familiarity withi their string theory chapters, but I have my reservations about any treatment of string theory that doesn’t begin with or assume some conformal field theory.
  3. Wess and Bagger, Supersymmetry and Supergravity. This is another of the classics. It has short, terse chapters which with a lot of detail left to the reader. On the other hand, it does manage to squeeze in some very subtle insight on how to approach supersymmetry. It can be a bit technical for my tastes, but I’ve heard that it’s one of the few books of its sort that “almost certainly contains no errors.” This is also an excellent reference for supergravity (local supersymmetry).
  4. Aitchison, Supersymmetry in Particle Physics: An Elementary Introduction. Published very recently with surprisingly little blogosphere buzz, Aitchison’s text looks like a slightly student-friendlier version of Bailin and Love. Aitchison claims his approach is “intuitive and constructive” rather than “formal and deductive” (an example of the latter is Wess and Bagger). I haven’t gone through this text in much detail as it doesn’t seem offer to much for one who has already worked through the fundamentals, however, I do wish this had been published a couple of years earlier when I could have used it. This would probably be my recommendation for a very first book on SUSY. The text itself appears to be based on a set of lecture notes which are available on the arXiv
  5. PDG. The PDG includes reviews of SUSY theory and experiment (look under Reviews > Hypothetical Particles and Concepts) which are regularly updated. Between you and me, I find the PDG to be excellent on-the-bus/train/bog reading. The pocket-version is like a booklet of flashcards for current experimental constraints. For those playing with their first models, the PDG is a great place to go when looking to constrain your parameter space.
  6. Quevedo, Supersymmetry and Extra Dimensions — Part III Lectures . Since I keep harping on about the Web 2.0 and science, I feel obligated to share this link to Prof. Quevedo’s Part III lectures on SUSY and extra dimensions. These fantastic lectures were calibrated to resonate with first year theoretical physics students who had just finished a one-semester QFT course. Unfortunately, at the time of this writing only a couple of lectures have been posted online. Keep an eye out, however, since these will probably be the first complete (24 lectures) supersymmetry course provided online via streaming video. (For shorter video courses on SUSY, check the usual physics video resources, especially those at Fermilab, CERN, and the SLAC summer institiute)

Here are some review articles which are shorter than any of the texts above, but that may be helpful for particular topics.

  1. Murayama, Supersymmetry Phenomenology. This is a relatively light review, but I especially like the approach to motivating supersymmetry. Instead of looking at loop diagrams, Prof. Murayama appeals to another UV problem, the singularity in the Coulomb potential which is solved by introducing antiparticles. The paper covers a broad range of phenomenological aspects, but these days one will find more discussion and detail in either Martin’s Supersymmetry Primer or the texts by Drees et al. or Baer and Tata (see above).
  2. Lykken, Introduction to Supersymmetry . Prof. Lykken’s TASI ’96 lectures give the usual introduction and quickly touches on several more foral topics: extended SUSY, BPS states, supergravity, higher dimensions. The TASI ’96 school was, after all, on string theory. (Odd-numbered years are phenomenological.) I would think that the second half of these lectures would be helpful for a beginner who wants to get a taste of what lies beyond the basics.
  3. Argyres, Lectures on Supersymmetry. There are actually two pairs of SUSY lectures here. The introductory lectures focus on N=1 supersymmetry in 4D. They’re available in 4-component (newer) and 2-component spinor notation. Also on Prof. Argyres’ page are notes on extended SUSY. Chris, my aforementioned token string theory buddy, recommends Argyres for those who don’t mind bypassing the MSSM. (You can just skip the phenomenological bits, apparently.) The `advanced’ topics start at chapter 2 and include anomalies/instantons, non-renormalisation of gauge theories, superconformal invariance, and duality.
  4. Haber, Introduction to Low Energy Supersymmetry. These lectures from TASI ’92 must be one of those `classic oldies.’ I haven’t had the chance to go through these in detail, but Prof. Haber has a well-earned reputation for thoroughness and insight.
  5. Haber and Kane, The Search for Supersymmetry: Probing Physics Beyond the Standard Model. The `classic’ review on supersymmetry is older than most of the students who are just starting to learn the subject. Understandably, developments in SUSY and SUSY pedagogy have changed with the times, though the review’s appendices have gone a long way to contribute to its timelessness. Included is a full set of MSSM Feynman rules as well as sample calculations. It’s a shame that not many review articles contain sample calculations these days.
  6. Drees, Introduction to Supersymmetry. A quick look through this set of lecture notes suggests it gives the `standard’ treatment outlined above, starting from the SUSY algebra, getting to the MSSM, and mentioning a few directions beyond the MSSM. You’d get the same material reading any of the `canonical texts for beginners’ listed above, though these lecture notes have the benefit of only being 43 pages long.
  7. Olive, Introduction to Supersymmetry: Astrophysical and Phenomenological Constraints. These Les Houches ’99 notes spend about 30 pages repeating the standard SUSY introduction before going into more unique details about cosmological constraints. This was a niche of the introductory literature that wasn’t really addressed by textbooks until the recent books by Drees et al., Binetruy, and Bailin and Love (their cosmology book).
  8. Peskin, Supersymmetry in Elementary Particle Physics. This is the newest item on this list, just posted on the arXiv two months ago. These TASI 06 lecture notes give a nice account of grand unification in the MSSM as well as some collider and dark matter phenomenology. If you want, you can go ahead and glue these lectures to the end of your copy of Peskin and Schroeder.
  9. Ryder, Quantum Field Theory (Chapter 11). If you’re not keen on stapling Prof. Peskins TASI notes to the end of his QFT text, here’s another excellent field theory book that comes with a SUSY discussion prepackaged into its last chapter. It’s a quick treatment but one that might be just right if you’ve read Prof. Ryder’s other 10 chapters anyway.

For pen-and-paper phenomenologists, there are a few reviews relevant for doing MSSM calculations. These generally replace Haber and Kane above, whose Feynman rules and treatment of Majorana fermions leave a bit to be desired (or so I’m told).

  1. Rosiek, Complete set of Feynman Rules for the MSSM. See Prof. Rosiek’s page for the most recent version. A set of consistent Feynman rules for the MSSM written out clearly once-and-for-all. (By the way, I might as well mention it now: you should know a thing or two about linear algebra, such as singular value decomposition and Takagi factorisation. Otherwise you might be confused about the way some of the matrices are diagonalised.)
  2. Denner et al., Compact Feynman Rules for Majorana Fermions and Feynman Rules for Fermion-Number-Violating Interactions. (I found the second one more useful.) Feynman diagrams with Majorana fermions are a bit tricky because there’s no well defined fermion number flow, and hence the arrows on Dirac propagators don’t mean anything on Majorana spinors.
  3. Nishi, Simple derivation of general Fierz-type identities; and Nieves and Pal, Generalized Fierz identities. These end up being very helpful for doing `real’ calculations, for example when calculating an effective Lagrangian for heavy flavour physics.šŸ™‚
  4. Borodulin et al., CORE 2.1. While I’m going on about doing calculations, this rather hefty reference might be helpful at one point or another. It’s also fun to skim through when you’re trying to look busy at your desk.
  5. Csaki, The MSSM. This 15-page mini-review of the MSSM doesn’t really hold a candle to any of the treatments above. However, I think it’s very important to highlight because it was originally written as a term paper for a SUSY course. Here’s some really important advice for young phenomenologists: if you want to really have a feel for the MSSM, then you need to do at least one of two things: (1) starting from a blank piece of paper, work out the entire structure of the MSSM (multiplets, superpotential, soft-breaking terms, mass eigenstates) and write down a list of MSSM Feynman rules; (2) write some computer code to take MSSM `top-down’ input parameters and calculate the spectrum and couplings of the mass eigenstates. By actually working through this `nitty gritty’ you’ll get a feel for how different parameters affect the low energy theory. Otherwise you’ll end up having to work out bits and pieces every time a seminar speaker mentions different regions of parameter space. As extra credit you can work out the RG running. Seriously: these are exercises that give you a feel for the MSSM. Presumably you did the same thing for the Standard Model at some point in your academic life.

Here are my favourite references for SUSY from a model-building perspective:

  1. Mohapatra, Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics. Now in its third edition, this book has very readable bite-sized sections on all sorts of neat topics. Introductory material on supersymmetry is a bit thin, but in its place there are lots of nice treatments of CP violation, unification, technicolour, supergravity. This isn’t the place to go for a comprehensive explanation, but it’s a great text for motivation and references.
  2. Binetruy, Supersymmetry: Theory, Experiment, and Cosmology. No, your copy of this book isn’t scuffed. The little white dots on the cover are supposed to represent stars, I think. This isn’t one of those books that you read from start to finish. The preface offers a few suggested reading programmes with various detours into the [very nice and thorough] appendices. Think of it as a `choose your own adventure‘ textbook for theorists/experimentalists/cosmologists. When I first did a self-study in supersymmetry, I found this nonlinearity a bit difficult since it was hard to motivate what was going on from one chapter to the next. However, as a reference for more advanced topics I think this text is excellent. There is are nice treatments of cosmology, supergravity, and duality complimented by detailed appendices that provide a self-contained exposition of the necessary background material.
  3. Drees et al., The Theory and Phenomenology of Sparticles. I’m not sure why more people don’t use the term `sparticles’ (it’s no worse than `sfermion’), but this text is a rather comprehensive text on SUSY phenomenology. The treatment is a bit more detailed for the calculationally-oriented. The first half of the book is, once again, the `standard treatment’ (plus supergraphs). The second half, however, goes on to talk about the MSSM and specific SUSY breaking schemes. There’s a lot of care put into the different sectors of the MSSM (diagonalising matrices, phenomenological implications), and the book ends with
  4. Baer and Tata, Weak Scale Supersymmetry. While Drees et al. is what I would consider a specialty-book for pen-and-paper theorists, Baer and Tata seems to have been written for those who intend to get down-and-dirty with programming. In fact, it’s the only book I found that had a chapter on SUSY event generation. There are lots of plots, references, and discussions of collider constraints. It might just be me, but I like to think of this as the sister volume to Drees et al.; there’s significant overlap in the basics, but they have complimentary approaches to everything else.
  5. Bailin and Love, Cosmology in Gauge Field Theory and String Theory. This is the second Bailin and Love text mentioned here, and it also happens to have `and String Theory’ attached to the end of it. I suspect this may have been the IOP’s attempt to break the Cambridge University Press monopoly of string books in the late 90’s. Anyway, this text comes highly recommended by Ben of Berkeley. These days the line between particle theory and cosmology is blurring, and any self-respecting SUSY model-builder should be fluent in the relevant aspects of cosmology. This text does a good job of highlighting the topics on this cosmo-particle interface, including LSP dark mattter, SUSY GUT phase transitions in the early universe, supergravity blackholes, and inflation.
  6. Kolb and Turner, The Early Universe. Okay, so this isn’t strictly a SUSY book. I’m not even sure if they mention SUSY. However, it is the original reference for astro/cosmo-particle physics and still has (to the best of my knowledge) the most complete treatment of relic densities.
  7. Chung et al., The Soft-SUSY-Breaking Lagrangian: Theory and Applications. This is a nice review that starts with the MSSM and goes on to discuss various SUSY-breaking schemes and constraints from flavour/ precision/ astroparticle/ cosmological/ collider constraints. An excellent range of topics.
  8. Dine, Supersymmetry and String Theory: Beyond the Standard Model. I think of this as a more-modern version of Mohapatra (which itself was recently updated). The topics spanned and focus on insight rather than detail are very similar. This is not a first book for supersymmetry (and certainly not for strings). However, it’s a great presentation of topics at the interface of supersymmetry between the Standard Model (phenomenological/model-building) and string theory (top-down/formal).

And now for some `advanced topics‘ (these are generally written for theorists, while most of the above literature should be accessible to SUSY-minded experimentalists). For more on supergravity, I would recommend Wess and Bagger [see above] as a starting point. For more on stringy physics, see Dine for a taste and a `real’ pedagogical string theory book for a complete treatment (see, e.g. Polchinski, Becker-Becker-Schwarz, Kiritsis, Johnson, … if you’ve already learned supersymmetry then Zwiebach may be too elementary).

  • Terning, Modern Supersymmetry. As mentioned above, this was recommended as a good textbook (supplemented by Argyres) for string theorists or formal theorists who are less interested in the MSSM. The range of topics focuses on duality, dynamical SUSY breaking, and recent formal developments in SUSY makes this a great book to have for anyone looking to go beyond the `standard’ SUSY treatments.
  • Terning. Nonperturbative Supersymmetry. TASI 2002 lectures that, I suspect, were the nucleus of the author’s textbook mentioned above.
  • Weinberg, The Quantum Theory of Fields, volume III. If you’ve gotten this far in studying field theory, you should already know what to expect from Weinberg’s third volume. Like his first two volumes, this book presents much of the `standard treatment,’ only packed with insights from every direction. Phenomenologically-oriented readers can go straight to chapter 26.
  • Nilles, Supersymmetry, Supergravity and Particle Physics. A rather old review, but it seems to commit a lot of pages to supergravity, which is a lot more than I can say for a lot of the modern literature.

For those that don’t like the standard treaments of anything, here are a few orthogonal approaches:

  • Gates et al., Superspace, or one thousand and one lessons in supersymmetry. Published in 1983 and now on the arXiv for free. They take an interesting pedagogical approach of exploring 2+1 dimensional supersymmetry as a toy model and working everything through including supergravity. The SUGRA material, by the way, seems to be the strength of the text in the current landscape of literature. As you can see from the list above, it’s easy to find review articles for the MSSM. It’s a little harder to find a detailed treatment of supergravity.
  • Siegel, Fields. A dramatically bold treatment of field theory that includes SUSY (rather early on), lots of representation theory, and string theory. It is as unorthodox as it is broad, but Prof. Siegel has clearly put a lot of thought into his pedagogical approach. The best way to get a feel for the book is the read the preface which includes a thorough discussion of how Fields is different from anything else out there, and why that’s good.
  • Varadarajan, Supersymmetry for Mathematicians. I think the title of the book says it all. Books like this highlight the differences between theoretical physics students and mathematics students.šŸ™‚

For semi-completeness, I should mention a few oldies that may be helpful:

  • West, Introduction to Supersymmetry and Supergravity. Unfortunately I haven’t really had a chance to skim through this book, though the new SUSY books in the past few years may push this 1990 text closer to retirement. I have, however, heard some good things about this book’s presentation of supergravity.
  • Sohnius, Introducing Supersymmetry. Another oldie. This one goes on to discuss conformal SUSY, N=2,4, SUSY in higher dimensions. (Remarkably prescient for it’s time as it was published well before the 1998 `XD revolution.’)
  • Fayet and Ferrara, Supersymmetry. One more review that looks really old. A quick look suggests that it doesn’t seem to add anything that’s not already covered in more recent texts (usually with better pedagogy).

    Finally, while you’re doing your academic reading, it’s often fun and instructive to learn a bit of SUSY history. This is for a few reasons. (1) Historical accounts are usually very conceptual and focus on how big ideas piece together. (2) You can often find some very enjoyable and candid stories about the people whose names are on important theorems. (3) As a young researcher looking to contribute to the current boundaries of physics, it helps to read how past pioneers dealt with the open questions of their time. I haven’t spent as much time looking for historical literature, but here are two that I liked:

    • Weinberg, The Quantum Theory of Fields Vol III, chapter 1. The first chapter of Weinberg III is a broad historical account of the development of SUSY. For a long time this was the only chapter of Weinberg that I was able to read.šŸ™‚
    • Kand and Shifman, The Supersymmetric World: The beginnings of the theory. This was my bedtime reading during Prof. Quevedo’s Part III SUSY course (see above). It’s at just the right level for someone actively learning supersymmetry. [Edited 26 Mar 08: I had mistakenly referred to `The Many Faces of the Superworld,’ also edited by Shifman. (The historical section of this other book might also be of interest.)]

    Going beyond the basics
    For most students, a small subset of the above literature will be enough to get you up-to-speed with current research. For those looking for literature on more advanced topics, I suggest checking the usual repositories. An excellent collection is hosted by the String Wiki: Supersymmetry and Supergravity (I can’t salute Tom and the Queen Mary string students enough for setting up this excellent resource for the community.) An older static collection can be found at SPIRES: HEP reviews, note that SUSY/SUGRA is split between Mathematical Physics and Beyond the Standard Model. Finally, there are SUSY/SUGRA entries at the Net Advance of Physics. (The benefit of the older collections is that they include older review literature that was published before the arXiv era.) These three resources should get you going in topics ranging from supergravity, supersymmetric solitons, duality, superconformal theories, dyamic supersymmetry breaking, and all sorts of other fun topics.

    15 Responses to “Introductory supersymmetry literature for the perplexed”

    1. 1 ND

      Hey, Thanks! It’s uncanny how timely this article is for me. Although, can you tell me roughly how long it should take one to get through the basics? (The prerequisites are done of course.)

    2. The Part III SUSY course mentioned above got through the basics in about twelve one-hour lectures (including an hour for historical motivation!). If you’re in a hurry, the first 3 chapters of Bailin and Love go over the `core’ of supersymmetry. Depending on your interests, you can skip extended supersymmetry and nonrenormalisation theorems. For even quicker presentations, pick one of the shorter review articles (Peskin, Lykken, or the last chapter of Ryder’s text) as your main guide and fill in the details with selected auxilliary reading. Good luck! (And study with a friend or two, it really helps.)

    3. 3 Rien

      Great post! I think that if you’re a phenomenologist it makes sense to read Martin and Murayama first to get a broad picture and details about what to expect and to understand some of what you read in papers, and then plow into Bailin & Love or something similar. O’Farrill, who you mentioned above, has a nice set of lecture notes too, that are pretty different from anything else I’ve seen (I was a guinea pig at BUSSTEPP).

      About representations: I like the treatment in QFT in a nutshell for a quick first overview (though I didn’t read that when I learnt it). Willenbrock has some useful TASI lectures on spinors, but he doesn’t use dotted/undotted. It’s hep-ph/0410370.

    4. Hi Flip!
      Just thought I should mention
      ‘Ideas and methods of supersymmetry and supergravity’ by Buchbinder and Kuzenko. Although it’s definitely not in the phenomenological direction it does cover the central issues very well. The first sections of the first chapter are all about reps of the Poincare group and two-component spinors. It’s probably the best treatment of this that I know.
      The third edition is apparently coming out fairly soon.
      Thanks for the post, I’m off to read that review by Terning that you mentioned!

    5. Thanks for the heads-up Simon! [ Alison mentioned at lunch that she knew someone who read my blog.šŸ™‚ ]

    6. Yeah, I was just explaining to Ali what I don’t know about spurions when she left to have lunch and a better conversation with you!
      I’m up to section 4 of Terning’s TASI lectures…. The holomorphy arguments always feel like cheating to me… I guess I just don’t grok them yet!

    7. 7 theoreticalminimum

      I would suggest 2 books by an exceptional physicist, Prof Gordon L. Kane, only one of which I have read to some extent:
      The Supersymmetric World: The Beginnings of the Theory* (historical, anecdotal, with technical accounts; one book which I am still reading when I need to hear a story), and
      Supersymmetry: Unveiling the Ultimate Laws of Nature ** (a more accessible – “popular” level – book, which some of your readers might enjoy. I might read it one day… )

    8. Ah! `The Supersymmetric World” was the book I read last year… I had mistaken it for another book Prof. Shifman edited. (Let me fix my post.) It is indeed a splendid text. The cover art, however, could use an explanation. (I think it was painted by a relation of Shifman’s?)

    9. 9 john


      Can someone tell me a good place where fierz rearrangement identities are actually worked out, e.g. the solution to problem (2) of chapter III of Wess and Bagger and the like?


    10. 10 john

      Never mind, I guess the article by Nishi, “Simple derivation of general Fierz-type identities”, has what I need.

    11. 11 Aqil Sajjad

      With reference to representations of the Lorentz group and spinors, Mark Srednicki provides a very good introduction in his QFT text. In fact, his book is a very friendly introduction to QFT. He tries to be as explicit as possible and skips very few steps, which makes it easy to follow. I also really liked his introduction to renormalization.

      The draft version of his book is actually available on-line. The intro to spinors is in part 2 (which covers spin 1/2 particles):

      part 1 (spin 0) is at

      Part 3 draft can be downloaded from his homepage.

    12. 12 Aqil SajjadAqil Sajjad

      Also, I was wondering if someone can suggest a treatment of spurions

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