Discrete gauge symmetries and the weak gravity conjecture

Journal Article · 23 May 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP05(2019)140 · OSTI ID:1602218

Craig, Nathaniel ^[1]; Garcia, Isabel Garcia ^[2]; Koren, Seth ^[1]

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1. Univ. of California, Santa Barbara, CA (United States)
2. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics

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 Z_N and Z$$N\atop{2}$$ 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 M_Pl.

• Research Organization: Univ. of California, Santa Barbara, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP); Gordon and Betty Moore Foundation; National Science Foundation (NSF)
• Grant/Contract Number: SC0011702; SC0014129; GBMF7392; PHY-1748958
• OSTI ID: 1602218
• Journal Information: Journal of High Energy Physics (Online), Vol. 2019, Issue 5; ISSN 1029-8479
• Publisher: Springer BerlinCopyright Statement
• Country of Publication: United States
• Language: English