Discrete gauge symmetries and the weak gravity conjecture
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Springer
Received: January 28, Revised: May 1, Accepted: May 6, Published: May 23,
2019 2019 2019 2019
Nathaniel Craig,a Isabel Garcia Garciab and Seth Korena a
Department of Physics, University of California, Santa Barbara, CA 93106, U.S.A. b Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle’s mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that ‘gravity is the weakest force’. Here, we take a step towards making this expectation more precise by studying ZN and ZN 2 gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to MP l . Keywords: Black Holes, Discrete Symmetries ArXiv ePrint: 1812.08181
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2019)140
JHEP05(2019)140
Discrete gauge symmetries and the weak gravity conjecture
Contents 1 Introduction
1
2 No remnants stabilized by discrete charge 2.1 Non-perturbative black hole arguments 2.2 Effect of discrete hair on black holes
4 4 6 8 8 10
4 Naturalness in the Swampland
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5 Conclusions
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1
Introduction
The Weak Gravity Conjecture (WGC) [1] states that a U(1) gauge theory consistently coupled to gravity must contain a particle with mass m and charge g satisfying gMP l m≤ √ . (1.1) 4π √ In what follows we ignore the factor of 4π and use m . gMP l , as O(1) refinements have no bearing on our discussion. Because this charge-to-mass-ratio is larger than that of an extremal black hole (BH), the corresponding state is referred to as being ‘super-extremal’. Since the electrostatic force between two such particles overcomes their gravitational attraction, the WGC can be recast as the statement that ‘gravity is the weakest force’. Motivation for the conjecture stems from the same type of considerations that question the viability of global symmetries in a theory of quantum gravity, namely the potential presence o
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