Standard model vacua for two-dimensional compactifications

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.

Section: Jhep06(2018)051mentioning

confidence: 85%

“…Even though V is not minimized with respect to all the variables at the vacua of the theory, we will still call it potential. The conditions for AdS 2 vacua are (see [41,60] for details):…”

Section: The Sm On the T 2 Torusmentioning

confidence: 99%

Section: The Sm On the T 2 Torusmentioning

confidence: 99%

See 1 more Smart Citation

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

Gonzalo

Herráez

Ibáñez

2018

“…More generally one can consider compactifications on general Riemann surfaces. Those have been argued in [6,8] not to lead to new vacua. The same has also been argued to be the case of 1D vacua [7]) (quantum mechanics).…”

Section: Ads Casimir Sm Vacua In 3dmentioning

confidence: 98%

“…[6] Arkani-Hamed et al explored this deep infrared SM region by making the interesting exercise of exploring the possible vacua that could be obtained by compactifying the SM action to lower dimensions. They found that there is a richness of vacua, a real landscape of vacua, both with AdS and dS geometries in 3D and 2D (see also [7,8] for low < 3D SM compactifications). The potential for the moduli of the compactification is induced by the Casimir effect of the lightest particles of the SM.…”

Section: /4mentioning

confidence: 99%

Constraining neutrino masses, the cosmological constant and BSM physics from the weak gravity conjecture

Ibáñez

Lozano²,

Valenzuela

2017

It is known that there are AdS vacua obtained from compactifying the SM to 2 or 3 dimensions. The existence of such vacua depends on the value of neutrino masses through the Casimir effect. Using the Weak Gravity Conjecture, it has been recently argued by Ooguri and Vafa that such vacua are incompatible with the SM embedding into a consistent theory of quantum gravity. We study the limits obtained for both the cosmological constant Λ 4 and neutrino masses from the absence of such dangerous 3D and 2D SM AdS vacua. One interesting implication is that Λ 4 is bounded to be larger than a scale of order m 4 ν , as observed experimentally. Interestingly, this is the first argument implying a non-vanishing Λ 4 only on the basis of particle physics, with no cosmological input. Conversely, the observed Λ 4 implies strong constraints on neutrino masses in the SM and also for some BSM extensions including extra Weyl or Dirac spinors, gravitinos and axions. The upper bounds obtained for neutrino masses imply (for fixed neutrino Yukawa and Λ 4 ) the existence of upper bounds on the EW scale. In the case of massive Majorana neutrinos with a see-saw mechanism associated to a large scale M 10 10−14 GeV and Y ν 1 10 −3 , one obtains that the EW scale cannot exceed M EW 10 2 − 10 4 GeV. From this point of view, the delicate fine-tuning required to get a small EW scale would be a mirage, since parameters yielding higher EW scales would be in the swampland and would not count as possible consistent theories. This would bring a new perspective into the issue of the EW hierarchy.

A dS obstruction and its phenomenological consequences

Riet

Venken

2020

In this note we observe that positive runaway potentials can generically be stabilized by abelian p-form fluxes, leading to parametrically controlled de Sitter solutions after compactification to a lower dimension. When compactifying from 4d to 2d the dS solutions are metastable, whereas all higher dimensional cases are unstable. The existence of these dS solutions require that a certain inequality involving the derivatives of the potential and p-form gauge coupling is satisfied. This inequality is not satisfied in simple stringy examples (outside of the scope of Maldacena-Nuñez), which unsurprisingly avoid this route to dS solutions. We can apply our techniques to construct dS 2 solutions in the Standard Model plus an additional runaway scalar such as quintessence. Demanding that these are avoided leads to (weak) phenomenological constraints on the time variation of the fine structure constant and QCD axion-photon coupling.