A note on Gauge Theories Coupled to Gravity

TL;DR

This paper discusses a semi-classical derivation of a bound on gauge couplings in theories coupled to gravity, valid in four or more dimensions, with implications for non-abelian and discrete symmetries, and checks in string theory.

Contribution

It provides a simple semi-classical derivation of the gauge coupling bound and explores its validity across different dimensions and symmetry types.

Findings

The bound e ≥ m/m_p can be derived from semi-classical considerations.

Non-abelian gauge symmetries naturally satisfy the bound.

Checks in string theory support the bound in higher dimensions.

Abstract

We analyze the bound on gauge couplings $e\geq m/m_p$, suggested by Arkani-Hamed et.al. We show this bound can be derived from simple semi-classical considerations and holds in spacetime dimensions greater than or equal to four. Non abelian gauge symmetries seem to satisfy the bound in a trivial manner. We comment on the case of discrete symmetries and close by performing some checks for the bound in higher dimensions in the context of string theory.