AdS-phobia, the WGC, the Standard Model and Supersymmetry

Abstract

It has been recently argued that an embedding of the SM into a consistent theory of quantum gravity may imply important constraints on the mass of the lightest neutrino and the cosmological constant Λ 4 . The constraints come from imposing the absence of any non-SUSY AdS stable vacua obtained from any consistent compactification of the SM to 3 or 2 dimensions. This condition comes as a corollary of a recent extension of the Weak Gravity Conjecture (WGC) by Ooguri and Vafa. In this paper we study T 2 /Z N compactifications of the SM to two dimensions in which SM Wilson lines are projected out, leading to a considerable simplification. We analyze in detail a T 2 /Z 4 compactification of the SM in which both complex structure and Wilson line scalars are fixed and the potential is only a function of the area of the torus a 2 . We find that the SM is not robust against the appearance of AdS vacua in 2D and hence would be by itself inconsistent with quantum gravity. On the contrary, if the SM is embedded at some scale M SS into a SUSY version like the MSSM, the AdS vacua present in the non-SUSY case disappear or become unstable. This means that WGC arguments favor a SUSY version of the SM, independently of the usual hierarchy problem arguments. In a T 2 /Z 4 compactification in which the orbifold action is embedded into the B − L symmetry the bounds on neutrino masses and the cosmological constant are recovered. This suggests that the MSSM should be extended with a U(1) B−L gauge group. In other families of vacua the spectrum of SUSY particles is further constrained in order to avoid the appearance of new AdS vacua or instabilities. We discuss a possible understanding of the little hierarchy problem in this context.

The Swampland: Introduction and Review

“…An interesting possibility arises which is that the AdS instability conjecture may forbid the existence of this stable AdS vacuum, which translates into bounds on properties of neutrinos. The idea was first raised in [], and studied in detail in []. A particularly striking possibility is that it bounds the neutrino masses by the cosmological constant It was then pointed out in [] that this could lead to insights into the hierarchy problem since the neutrino masses are naturally tied to the scale of electroweak symmetry breaking.…”

“…In particular, in [] it was shown that one must add the Wilson line of the electromagnetic gauge field on the circle to the analysis, and this leads to an instability associated with the electron. In [] a possible way to remove the instability was considered by taking an orbifold compactification. It was then argued that the question of stability of the AdS vacuum would be related to physics of supersymmetry breaking.…”

IR dynamics from UV divergences: UV/IR mixing, NCFT, and the hierarchy problem

“…this case that the λ 2 interaction term is no longer gauge invariant, and a charged scalar may only self-interact through V = λ 1 φ * φ φ * φ. Purely from gauge invariance we thus see that a fundamental scalar has no nonplanar self-interaction diagrams in the one-loop correction to its two-point function, and so there is no remnant of strong UV/IR duality to speak of. 15 The question is then whether there are other examples where this strong UV/IR duality does occur, or whether it is perhaps a peculiar feature of real φ n theories on noncommutative spaces. To answer this, we will study in detail another case of especial phenomenological significance: Yukawa theory.…”

“…While this is powerful information, the extent to which the UV here meddles with the IR is relatively minor -just dictating where one must live in the space of infrared theories. Even so, they have been found to have possible applications to SM puzzles, including the hierarchy problem [9][10][11][12][13][14][15][16][17][18].…”

The weak scale from weak gravity

“…The potential for the Swampland program, and adjacent developments, to explain some of the more puzzling features of the SM has been explored in e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17].…”