## Friday, May 15, 2009

### Life on intersecting heterotic fivebranes

There are many interesting hep-th papers on the arXiv today: reinterpretation of instantons as bound states of partons, a discussion of right-handed neutrinos in F-theory phenomenology, the complete (finite!) Ansatz for the four-graviton four-loop scattering amplitude of N=8 SUGRA, a refinement of the 1997 Cherkis-Schwarz derivation of the heterotic string from a K3-compactified fivebrane, and others.

While the rest of Asia seems to be working on the Hořava-Lifshitz gravity, Tetsuji Kimura and Shun'ya Mizoguchi are proposing a brand new phenomenological scenario to obtain a realistic gauge group and matter spectrum from string theory:
Yet another alternative to compactification - heterotic five-branes explain why three generations in nature
Recall that there exist several methods to obtain a realistic spectrum in 3+1 dimensions: heterotic strings on Calabi-Yau manifolds, Hořava-Witten heterotic M-theory on Calabi-Yau manifolds, F-theory singularities, M-theory singularities inside G2 manifolds, type IIA intersecting braneworlds, and generic F-theory compactifications in the "landscape" that generate the right spectrum "by chance".

I have included the last category only because it is favored by the anthropic people but I personally find it the least motivated one because its agreement with the detailed features of the observed Universe is minimal.

These two physicists try to propose a qualitatively new way to obtain the right spectrum, including the inevitably right number of generations. They say that the picture is an alternative to compactification: I wouldn't say that this is an accurate description. In order to get a finite Newton's constant in 3+1 dimensions, they still need to compactify the transverse dimensions (e.g. on a six-torus). The Japanese pair compares their setup to Randall-Sundrum one (with a guaranteed vanishing cosmological constant) but I don't quite understand the analogy.

But if correct, their picture is certainly a new scenario to describe where the matter fields are located in extra dimensions. The method is based on heterotic fivebranes and it may be the most convincing realization of the tantalizing decomposition of the E8 adjoint representation under the E6 x SU(3) subgroup,
248 = (78,1) + (1,8) + (27,3) + (27,3)
In some stringy sense, the E8 group is the likely "grandfather" of the observed Standard Model gauge group; the father in the middle is a GUT-like group. This statement about the E8 origin of all gauge groups is naturally supported by the heterotic models as well as the models with the F-theoretical singularities. I wouldn't bet 100:1 that this assumption is true but the probability that it's true is comparable to 50%.

So it makes sense to ask how its representations are decomposed. Of course, when the group is broken to a subgroup, the representations of the original large group may become meaningless. But they may still be "somewhere" because the symmetry breaking must always be, in some moral sense, spontaneous: later, this point will be used much more accurately. So it is very interesting that there seem to be three copies of a "27", i.e. three copies of a realistic GUT generation of fermions (and their superpartners).

Consider the E8 x E8 heterotic string theory. Its 9+1-dimensional spacetime is equipped with 16 supercharges and an E8 x E8 gauge group in the bulk. The theory includes fivebranes with 8 supercharges. The gauge field inside them may belong (let's hope!) to an SU(2) subgroup of one E8 which breaks the symmetry from E8 to E7, the centralizer of the SU(2). Recall that the fivebrane may be interpreted as an instanton in the heterotic gauge field.

Now, consider two intersection fivebranes, extended in the directions 0-34-789 and 0-56-789, respectively. They share the four-dimensional spacetime, 0-789, while the other four dimensions, 3456, are relatively transverse. (123456 are expected to be compactified, e.g. on a six-torus.) This configuration breaks the 16 supercharges of the bulk down to 4 supercharges, i.e. to the realistic N=1 supersymmetry in 3+1 dimensions. If the gauge connection around the intersection is identified with the spin connection, the E8 is broken to a centralizer of an SU(3), i.e. E6, and matter organizes into chiral multiplets.

Now, you could argue that the decomposition of 248 above becomes irrelevant because only E6, and not SU(3), is unbroken, and the number of zero modes transforming as an E6 representation doesn't have to be a multiple of three because the SU(3) as well as E8 is just gone. But don't forget about one of my comments above - and the insights of a 2008 physics Nobel prize winner. ;-)

What do I mean? There are Nambu-Goldstone bosons (and whole SUSY multiplets) from all the broken generators and these bosons (or multiplets) always care about the larger, broken group! Because E8 was reduced to E6, the components of (1,8), (27,3), and (27*,3*) should produce Nambu-Goldstone bosons. Because we have 162 of (27,3)-like broken generators, there must be 162 real scalar Nambu-Goldstone fields which, by SUSY, must be organized as the bosonic content of (27,3) worth of chiral multiplets (81 complex scalar fields!) while the (27*,3*) are just their CPT conjugates. This is not like the Higgs mechanism - the Nambu-Goldstone bosons should be chiral multiplets, not parts of massive vector multiplets.

If this reasoning is true, it's a possible natural explanation of the three generations we observe by string theory. All the matter fields would arise from the moduli describing how an E6 is embedded into an E8, and their superpartners. You can see that this paragraph sounds like a group-theoretical one, so it may hold in some dual descriptions (besides the heterotic fivebranes), too.

The authors also add comments about a possible Scherk-Schwarz compactification to break SUSY, orbifolding, and similarities with RS1. But I would say that these additions are "optional", increasingly uncertain, and they're not essential for the main picture that they propose.