A search of stringy maths tachyon papers brought to light this fantastic 2004 paper, with tachyons appearing when legs cross in a $(p,q)$ web diagram.

Looks familiar, doesn't it? These webs are supposed to describe stringy brane configurations, but as usual we will think of them as toric variety diagrams. The paper discusses getting rid of tachyons, but do we need to?

6 years ago

Very nice; that gives me a way to think about your tetractys diagrams.

ReplyDeleteEarlier papers: 1 2 3.

A few days ago, Philip Candelas gave a talk on the Calabi-Yau spaces currently exciting interest among those mainstream string phenomenologists who aren't doing anthropic landscape calculations... He highlights two mirror-symmetric CYs with close to minimal Hodge numbers. I think what they want to do is take a quotient of the CY by some discrete symmetry, then wrap flux around one of the remaining noncontractible topological cycles. That is, the model-building choices are the choice of quotient and the choice of flux.

ReplyDeleteI see that in the original paper on describing brane configurations with toric skeletons, section 4, they claim that these methods can provide an intuitive explanation of mirror symmetries (which are T-dualities), such as those connecting Candelas's favorite CY with its mirror.

These models are being constructed under the usual phenomenological assumptions, such as the supersymmetric standard model with broken supersymmetry. But it would be very interesting if one could adjust them a little and end up with phenomenological tachyons. And it wouldn't hurt for these people to look at your gravity paper, linked above, with an open mind...

Just to be more specific: it's an old idea that the super-partner of the neutrino might be the Higgs. Our blog-host, meanwhile, is employing a categorical generalization of Bilson-Thompson's scheme associating braids with standard model fermions.

ReplyDeleteOne way forward would be simply to associate the braids with N=1 superfields. The algebraic category would be a superalgebra, in some sense. But another way would be to employ the "mirror neutrinos" (neutral braids unused in Bilson-Thompson's original scheme) as the source of mass.

I have no idea how far one can get by trying to close the gap between a Sheppeard mirror neutrino and a sneutrino down-type Higgs. But I want to point out one thing, which is that Witten's recent construction of Khovanov homology within M-theory (elaborated in a paper with Gaiotto) employs 5-dimensional gauge theories with a 4-dimensional limit, just like the theories in the paper in this post. In fact, I think the connection runs deeper, in that the cigar geometry employed at the 6-dimensional level also lies at the beginning of holographic QCD.

I don't actually know whether particles-as-braids and particles-as-branes can meet in five dimensions - which seems to be what is required for these two programs to make contact. Then again, Witten's knots are Wilson loops (or dual 't Hooft operators), and it seems that strings can sometimes arise as the holgoraphic dual of a Wilson line. It's not impossible that strings-between-branes on a noncontractible space have a dual description as knots in another space, especially if twistor transformations are involved.

Phillip is a very nice guy in person, but I doubt he is about to give up string theory just because I said so (although he should).

ReplyDeleteGood comments, Mitchell, but you are still failing to see that geometry is emergent. The twistor picture is in 'another space' entirely, indeed. Notice that I am talking about polytopes etc, which is utterly different to what Witten does with 5-branes. They extend into infinite dimensions. That said, it couldn't hurt for someone to do what you say.

I am not about to take sparticles seriously, but the string picture may help piece together the Higgs terms in the SM Lagrangian (a tachyon term plus a mirror pair quartic term).