Musings

Renata Kallosh talked about flux stabilization on $K3\times K3$. In the presence of fluxes, there are Euclidean D3 instanton (in M-theory, M5 instanton) corrections to the superpotential from divisors of arithmetic genus $\chi_{\mathcal{O}}=2$. In the absense of fluxes, only $\chi_{\mathcal{O}}=1$ contribute instanton corrections (though, in general, positive $\chi_{\mathcal{O}}$ can make “fractional instanton”, AKA gaugino condensate, contributions to the superpotential).

In the presence of flux, some of the zero modes are lifted, and higher values of $\chi_{\mathcal{O}}$ contribute instanton corrections. Aspinwall and Kallosh used this to fix all the moduli in compactification of M-Theory on $K3\times K3$ (where the relevant divisors, of the form $\mathbb{P}^1\times K3$ and $K3\times\mathbb{P}^1$, have $\chi_{\mathcal{O}}=2$).

Tomasiello gave a beautiful talk on his work with Graña et al on generalized complex geometry and N=1 supersymmetry in Type II compactifications with flux. I’ve meant to blog about Gualtieri and Hitchin’s work on Generalized Complex Structures for a while now. Maybe I’ll get around to it someday.

The afternoon was rather phenomenological, with a talk by Witten on axions in string theory and a talk by Arkani-Hamed on LHC physics. The “surprise” of Witten’s talk was that, really, there was no surprise. The axion decay constant, $f_a$, in the “new” string theory backgrounds is really not much different from that in the string backgrounds we knew about 20 years ago. With the notable exception of heterotic backgrounds with anomalous $U(1)$s, the typical value of $f_a\sim 10^{16}$ GeV. This has always been somewhat in conflict with purported cosmological upper bound, $f_a \lesssim 10^{12}$ GeV (which comes from demanding that axions not dominate the energy density)¹. On the other hand, as noted by Banks et al, this cosmological upper bound is easily evaded.

Arkani-Hamed’s talk was a bit more upbeat. The prospects for extracting physics at the LHC are quite exciting. He discussed both “natural” theories (low-energy supersymmetry, little Higgs models, …) and “unnatural” ones (split supersymmetry), and what sort of signatures one could expect. The map, alas, from parameter space, in low-energy supersymmetry, to “signature space” is many-to-one. Sorting this out is the subject of the LHC Olympics.

No, I’m not going to talk about the panel discussion, except to mention Joe Polchinski’s quip about “Anthropic/CFT Duality.”