Stringy origin of non-Abelian discrete flavor symmetries

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.

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“…Those may appear in string compactifications as gauged R-symmetries, see e.g. [65][66][67][68][69][70].…”

Section: Embedding Z 4 Into Discrete Gauge Symmetriesmentioning

confidence: 99%

“…R-symmetries of this type are also abundant in string theory [65][66][67][68][69][70]. In some cases they are gauged in the σ-model sense, and their anomalies are cancelled by a Green-Schwarz mechanism, see e.g.…”

Section: Embedding Into the U(1) S R-symmetrymentioning

confidence: 99%

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

Gonzalo

Herráez

Ibáñez

2018

J. High Energ. Phys.

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“…Moreover, it has recently been argued that discrete symmetries appear abundantly in string model constructions [15][16][17], with important applications for particle physics model building [18][19][20][21][22]. We are thus in a situation that P 6 could originate from a string model as consistent UV completion and that such a symmetry is compatible with local grand unification.…”

Section: Introductionmentioning

confidence: 99%

Proton hexality in local grand unification

et al. 2010

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“…For some recent dedicated discussions on discrete symmetries in string theory, see e.g. [39][40][41] for heterotic examples and [42][43][44][45][46] for D-brane examples. We have to specify the representations of the various fields under the flavour group G × U(1), where G is a discrete subgroup of SU (2).…”

Section: The Modelmentioning

confidence: 99%

Linking natural supersymmetry to flavour physics

Dudas

Gersdorff

Pokorski

et al. 2014

J. High Energ. Phys.

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With the aim of linking natural supersymmetry to flavour physics, a model is proposed based on a family symmetry G × U(1), where G is a discrete nonabelian subgroup of SU(2), with both F-term and (abelian) D-term supersymmetry breaking. A good fit to the fermion masses and mixing is obtained with the same U(1) charges for the left-and right-handed quarks of the first two families and the right-handed bottom quark, and with zero charge for the left-handed top-bottom doublet and the the right handed top. The model shows an interesting indirect correlation between the correct prediction for the V ub /V cb ratio and large right-handed rotations in the (s, b) sector, required to diagonalise the Yukawa matrix. For the squarks, one obtains almost degenerate first two generations. The main source of the FCNC and CP violation effects is the splitting between the first two families and the right-handed sbottom determined by the relative size of F-term and D-term supersymmetry breaking. The presence of the large right-handed rotation implies that the bounds on the masses of the first two families of squarks and the right handed sbottom are in a few to a few tens TeV range. The picture that emerges is light stops and left handed sbottom and much heavier other squarks.

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Stringy origin of non-Abelian discrete flavor symmetries

Cited by 290 publications

References 48 publications

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

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

Proton hexality in local grand unification

Linking natural supersymmetry to flavour physics

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