## Tuesday, May 20, 2008

### Monad CICY heterotic landscape: 7118

There are several hep-th papers today that I find very interesting.

Ho, Imamura, Matsuo, Shiba (Taiwan and Tokyo) continue in the membrane minirevolution and interpret the Bagger-Lambert-Gustavsson action as an M5-brane action in a 3-form magnetic field, with all kinds of the obvious answers you would like or expect.

Alex Buchel (Perimeter Institute) argues that their 2005 claims about a different subleading correction to the AdS/CFT-derived entropy-density-to-viscosity ratio were caused by a mistaken choice of the boundary conditions at the horizon. He fixes the mistake and the problem goes away: the new coefficient is confirmed.

Ding-fang Zeng (Beijing) calculates heavy quark potentials in three simple AdS/QCD models.

There are also papers about B-brane superpotentials, trace anomaly from AdS/CFT, heavy ion colissions from AdS/CFT, topologically charged membranes in AdS/CFT, N=8 SUGRA amplitudes, uniqueness of higher-spin gauge theories, supertwistors, solutions to modified Bianchi identity, Wess-Zumino gauge, RG flows applied to gravity (only dimensionless couplings can have universal behavior), and many others.

But I chose the following winner.

Lara Anderson, Yang-Hui He, and André Lukas (Oxford) classify positive monad heterotic E8 x E8 bundles on CICYs (complete intersection Calabi-Yau manifolds), topologies that can be defined - analogously to the quintic hypersurface - by polynomial equations in products of ordinary projective spaces and that still represent the most famous large ensemble of Calabi-Yau manifolds.

The paper is another fascinating example how dramatically the number of points on the landscape is reduced once certain conditions are imposed. Incidentally, Lara Anderson is an ingenious homeschooler originally from Utah but she was hijacked by Oxford via Rhodes.

First, they have to choose the geometric background - the CICYs. They have been classified: there are 7890 of them in total (although the present authors claim that 435 of them are redundant at the end of their paper). Anderson et al. make a pre-selection of those that have a chance to admit symmetry breaking by the Wilson lines: they only find 4515 "favorable" CICY geometries out of the 7890.

However, it must also be possible to construct a stable, anomaly-free bundle on them. Remember that they're searching for positive monad bundles; monad bundles are essentially kernels of maps between direct sums of line bundles (defined through short exact sequences). It turns out that only 36 out of the 4515 favorable CICYs admit positive monad bundles. However, there are typically several possible bundles for one CICY: in total, they find 7118 models.

They know how to calculate the particle spectrum for each. The Higgs fields only appear at special subspaces of the moduli spaces. There are never any anti-families. Among the 7118 models, 559 of them can lead to 3-generation models either directly or by orbifolding by a discrete group of order "k" (the Euler character must be a multiple of "k" and the original number of families must be "3k"). Most of these 559 models have a high value of "k", only 21 models have "k" smaller than 14.

When one deals with some classes of vacua that can be generated by an algorithm or simple enough rules and constraints, it is often rather straightforward (although with very fancy calculations only) to classify physics of all of them. A general question is whether we have any reason to expect that the compactification describing the world belongs to this special class or similar ones.

I think that this question is very important for our decision "where to look" and both answers are conceivable. The default "anthropic" answer is that we shouldn't expect anything like that. On the other hand, there can exist some very crisp dynamical mechanisms (or unknown consistency constraints) that make a constructible class much more likely or inevitable. Of course it would be nice to find such a rule. It is also important to avoid wishful thinking.

In summary, I find it very healthy if a subgroup of mathematicians and physicists focuses on the special cases because special cases are relevant more frequently than the generic ones.

And that's the memo.