## Thursday, June 27, 2019 ... //

### A three-parameter jungle of F-theory Standard Models

I want to mention two cool new papers now. First, a paper showing that natural supersymmetry is alive and well.

The current status of fine-tuning in supersymmetry
Melissa, Sascha Baron-Cohen (Borat), and Roberto (Holland+Kazakhstan+Spain – and I've sent a few more people to arXiv.org again LOL) have analyzed the degree of fine-tuning in supersymmetric models using two widely accepted formulae. They found out that totally natural SUSY models are compatible with the LHC exclusion limits – the degree of fine-tuning is just 3-40 or 60-600 for low-scale measure or high-scale measure, respectively.

The models get particularly viable if you look at the pMSSM (phenomenological minimal supersymmetric standard model – parameterized by a limited number of parameters close to the observations; I think it should have been expected) and the pMSSM-GUT is doing much better in fine-tuning than other GUT models. And when the fine-tuning depends primarily on the higgsino mass which may still be very low, and it's possible in huge regions of the parameter space, the fine-tuning may be very low.

Tons of writers if I avoid the more accurate term "lying or deluded inkspillers" have persuaded some 97% of the Internet users who care – it's my estimate based on the comments I am receiving – that the LHC has excluded natural supersymmetry. Well, the calculations in the actual experts' papers show something very different. This 39-page-long paper with 9 MB of graphs concludes in the abstract: "We stress that it is too early to conclude on the fate of supersymmetry/MSSM, based only on the fine-tuning paradigm."

So when someone tells you that the LHC has said something fatal about supersymmetry or naturalness, don't forget you are being lied to.

That was on hep-ph. The second paper I want to mention is on hep-th and is dedicated to a similar topic as a quadrillion Standard Models in F-theory in March:
Generic construction of the Standard Model gauge group and matter representations in F-theory
Like Cvetič et al. in March, Wati Taylor and Andrew Turner (MIT) look for promising realistic classes of F-theory compactifications.

Taylor and Turner demand the final gauge group to be the exact Standard Model gauge group$(SU(3)\times SU(2)\times U(1)) / \ZZ_6$ at all times. They like models with 6 uncompactified dimensions so they look at the F-theory models for those, assuming that the realistic 4D models are obtained as some compactification of two more dimensions from a 6D model that already has the correct gauge group.

In six dimensions, one has to satisfy the nontrivial anomaly cancellation conditions. Note that in this 6D-to-4D F-theory model building, the 6D model is almost completely described by a geometry (an elliptically fibered 3-fold) and it mostly specifies the gauge group. While compactifying to 4D, one may and must add some fluxes (which are "non-geometric" information), and these fluxes are correlated with the chiral matter that appears in 4D physics.

They impressively claim that if they assume the right gauge group above; the MSSM matter spectrum; six large dimensions; and the absence of tensor multiplets in 6D, they have a complete proof of having found all F-theory compactifications with these conditions. Somewhat less certainly, they want us to believe that even if the "no tensor multiplets" condition were relaxed, or if 6D were replaced by 4D, they could still do a similar classification.

A cool result is that the largest bunch of constructions obeying these conditions is a well-defined class of compactifications that are obtained by Higgsing $SU(4)\times SU(3)\times SU(2)$ F-theory models in 6D. This class is parameterized by 3 parameters: $b_3,b_2,\beta$. 71 such models exist when there are no tensor multiplets. Three bifundamental fields are involved in these vacua, various bases are possible.

You know, the three parameters are just integers and they have to obey inequalities$\eq{ 4b_3 + 3b_2 + 2\beta&\leq -8a\\ b_3+b_2+\beta &\geq -a }$ These inequalities bind the integers from both sides and there are 98 solutions. Geometries may be built for each etc. although I feel they only superficially mention the geometries – and their Fano bases and other bases etc. The paper is more field-theoretical than geometric in character.

It seems that the authors must really love the $SU(4)\times SU(3)\times SU(2)$ in 6D and trust it's a promising extension of the existing groups. It's not a Pati-Salam group – they also have some Pati-Salam realizations of the Standard Model – but this Taylor-Turner seems to be analogous to Pati-Salam and according to this analysis, it may be favored over Pati-Salam in F-theory.