- #1

mitchell porter

Gold Member

- 1,334

- 544

Here we have a new perspective on the issue:

https://arxiv.org/abs/2104.09682

**Is the Standard Model in the Swampland?**

Katsuki Aoki, Tran Quang Loc, Toshifumi Noumi, Junsei Tokuda

*[Submitted on 19 Apr 2021]*

Obviously no, leading to a necessary condition for quantum gravity. We study compatibility of the Standard Model of particle physics and General Relativity by means of gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity. In particular, we identify the cutoff scale of the Standard Model coupled to gravity by studying consistency of light-by-light scattering. While the precise value depends on details of the Pomeron effects in QCD, the cutoff scale reads 10^{16}GeV if the single-Pomeron exchange picture works well up to this scale. We also demonstrate that the cutoff scale is lowered to 10^{13}GeV if we consider the electroweak theory without the QCD sector.

This paper belongs to a recent genre which seeks theoretical (rather than empirical) bounds on the possible values of coefficients in quantum field theory, by making assumptions about the properties of an unknown deeper theory. In this case: "gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity".

Their conclusion is that new physics must enter between 10

^{15}-10

^{17}GeV. This is around the usual scale of grand unification theory, and not too far from the usual Planck scale (10

^{19}GeV).

Some considerations bearing upon the possibility of a desert:

First, a reminder of why grand unification is attractive: a single generation of the standard model neatly fits into a single multiplet of SU(5) or SO(10); and the running gauge couplings converge on similar values, around these high scales (as if they were all descended from a single coupling).

However, grand unification has the potential to spoil that prediction of the Higgs boson mass, or anything else which would attribute significance to the criticality of the electroweak vacuum. (One may see here an attempt, by a coauthor of that Higgs prediction, to have grand unification without the extra particles that spoil everything.)

Another problem is the tuning of the Higgs coupling that seems to be necessary to keep its mass light. Even just adding gravity is supposed to cause a tuning problem (since virtual black holes should be adding superheavy corrections to the observed mass), though perhaps this can be avoided in the right kind of gravitational theory.

Perhaps the main question I have regarding this new paper, is whether these familiar high scales have an independent origin in their argument. If they do, then their argument may tell us something new about what kind of theory naturally has a desert, namely, a theory which "saturates" their bounds, i.e. comes as close as possible to violating the positivity bounds.