For any of a million reasons I recently found myself reading Phys. Rev. D 28 1010, Analysis of anomalies in higher space-time dimensions by Frampton and Kephart. The paper derives the chiral anomaly in spacetime dimensions, and includes some neat polygonal Feynman diagrams such as this:
What really got me thinking, however, was a statement the authors made in the introduction to the paper:
We are very hesitant in invoking more than four dimensions since there is no direct experimental motivation. However, a leading candidate for a finite quantum gravity is proposed by the superstring which necessitates . If, as appears to us unlikely, any supergravity should be finite in , our motivation to consider would be correspondingly weakened.
Another important conceptual issue in considering is whether the higher dimensions are merely a mathematical device […] or are actual physical dimensions […]
So here’s a paper that’s a bit older than I am. It addresses extra dimensions, even though it was written just shortly after Rubakov and Shaposhnikov’s first papers on the brane-world scenario and a whole fifteen years before the ADD scenario made😄 models `cool’. Further, it points to motivation from superstring theory, even though it preceeded the first superstring revolution. As such, the paragraph highlights candid opinions on [what turned out to be] nascent `big ideas’ before they were hits.
(This is `cool’ in roughly the same way that listening to a rock band before they were popular is `cool,’ or the way cheering for a basketball player in the NCAA before they make it big in the NBA is `cool’.)
Here are a few of my own notes (corresponding to my numbering above) with the benefit of 20/20 hindsight:
(1) We are very hesitant in invoking more than four dimensions since there is no direct experimental motivation.
To this day we still don’t have any experimental motivation for higher dimensions, but we do have expected signatures that we’re looking for. These include mini black-holes, the CMB power spectrum, and Kaluza-Klein particles. What’s changed since then? In 1998 the ADD brane-world model linked extra dimensions to the hierarchy problem, which theorists had (by then) been using as a motivation for new physics. It turned out that braneworld theories had a rich model-space for theorists who were tired of playing with SUSY. Even without direct experimental motivation,😄 models are now common buzzwords for public outreach and nobody is ashamed to mention them as `motivation’ in a seminar talk.
(2) However, a leading candidate for a finite quantum gravity is proposed by the superstring which necessitates .
This paper was written just before the Green-Schwarz-led Superstring Revolution of 1984, so I suppose its authors had good noses for research directions. Today string theory is still the leading candidate for quantum gravity, though nobody in the 1980s could have expected the `string debate’ to ever become so (at times) heated or to spill over into popular culture. All the same time, papers today would have instead written this sentence as, “String theory predicts , so …”
(3) If, as appears to us unlikely, any supergravity should be finite in , our motivation to consider would be correspondingly weakened.
It wasn’t only a year (or two) ago that the finiteness of SUGRA became a hot topic. I haven’t kept up with developments on this front, but the last I heard of it was that there were some strong indications that SUGRA in is indeed finite. However, unlike what these authors seem to think, this has come off as more of a curiosity rather than a reason to abandon string theory. (I don’t quite understand the details of this, but it seems that SUGRA by itself is not a consistent theory of gravity?)
(4) Another important conceptual issue in considering is whether the higher dimensions are merely a mathematical device […] or are actual physical dimensions […]
Again, I’m stepping out of my domain of comfortable understanding, but this touches on (I think) what is now called deconstruction. (Pioneered by Georgi and friends.) The main idea is that one can play with a theory’s gauge group to make the theory mimic behavior in a higher-dimensional lattice. That is to say that the higher dimensions involved are `mathematical devices’ to explain lower-dimensional behavior. Deconstruction was one of the motivations for Little Higgs models.
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