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A note on Gauge Theories Coupled to Gravity

Tom Banks, Matt Johnson, Assaf Shomer

TL;DR

The paper derives a semiclassical bound $e \ge \frac{m}{m_p}$ on $U(1)$ gauge couplings in gravity by requiring charged black holes to discharge without violating entropy bounds, and shows this bound extends to $N+1 \ge 4$ dimensions. It demonstrates that global continuous symmetries are incompatible with quantum gravity because gauge interactions must enable BH discharge, with Hawking and Schwinger processes providing the mechanism. The authors test the bound in string theory contexts—Type I compactifications, D0-branes, and branes with higher-form charges—finding consistency in weakly coupled regimes and for BPS states, while noting triviality for non-abelian gauge theories in higher dimensions and subtleties for discrete symmetries. Overall, the work supports the view that quantum gravity forbids exact global symmetries and imposes gravity–gauge coupling constraints that survive dimensional and string-theoretic generalizations.

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.

A note on Gauge Theories Coupled to Gravity

TL;DR

The paper derives a semiclassical bound on gauge couplings in gravity by requiring charged black holes to discharge without violating entropy bounds, and shows this bound extends to dimensions. It demonstrates that global continuous symmetries are incompatible with quantum gravity because gauge interactions must enable BH discharge, with Hawking and Schwinger processes providing the mechanism. The authors test the bound in string theory contexts—Type I compactifications, D0-branes, and branes with higher-form charges—finding consistency in weakly coupled regimes and for BPS states, while noting triviality for non-abelian gauge theories in higher dimensions and subtleties for discrete symmetries. Overall, the work supports the view that quantum gravity forbids exact global symmetries and imposes gravity–gauge coupling constraints that survive dimensional and string-theoretic generalizations.

Abstract

We analyze the bound on gauge couplings , 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.

Paper Structure

This paper contains 20 sections, 48 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Global Symmetries in QG.
  3. No-Hair
  4. Hawking evaporation
  5. Black-holes and $U(1)$ gauge symmetries.
  6. The basic strategy
  7. Semi-classical discharge of Black Holes
  8. Small/Hot BHs - The Hawking process
  9. Large/Cold BHs - The Schwinger process
  10. Deriving the AMNV bound in $N+1$ spacetime dimensions.
  11. Hot BHs in $N+1$ dimensions
  12. Cold BHs in $N+1$ dimensions
  13. String theory consistency checks for $N>3$
  14. Type I String Theory on $\mathbb{R}^{1,9-d}\times \mathcal{M}^{(d)}$
  15. $D0$ branes in flat $\mathbb{R}^{1,9}$
  16. ...and 5 more sections

Figures (1)

  • Figure 1: The qualitative behavior of the bound.