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Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity

Alexandre Belin, Jan de Boer, Pranjal Nayak, Julian Sonner

TL;DR

The paper extends the eigenstate thermalization hypothesis to systems with global symmetries by proposing two variants—one enforcing microscopic charge conservation and another allowing exponentially small violations. It then connects these ideas to holography via Euclidean wormholes, showing that wormhole computations predict a nonzero variance for charged one-point functions when the bulk symmetry is global, which is incompatible with exact charge conservation; gauging the symmetry removes this variance. The work thus links ETH randomness, OPE coefficient statistics, and wormhole physics to argue that global symmetries cannot exist in quantum gravity (at least in AdS contexts) unless they are gauged or broken nonperturbatively. These results provide a gravitationally rooted constraint on global symmetries and clarify how charge-sector structure in ETH manifests in holographic and gravitational frameworks.

Abstract

We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present two versions, one with microscopic charge conservation and one with exponentially suppressed violations. They agree for correlation functions of simple operators, but differ in the variance of charged one-point functions at finite temperature. We then apply these ideas to holography and to gravitational low-energy effective theories with a global symmetry. We show that Euclidean wormholes predict a non-zero variance for charged one-point functions, which is incompatible with microscopic charge conservation. This implies that global symmetries in quantum gravity must either be gauged or explicitly broken by non-perturbative effects.

Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity

TL;DR

The paper extends the eigenstate thermalization hypothesis to systems with global symmetries by proposing two variants—one enforcing microscopic charge conservation and another allowing exponentially small violations. It then connects these ideas to holography via Euclidean wormholes, showing that wormhole computations predict a nonzero variance for charged one-point functions when the bulk symmetry is global, which is incompatible with exact charge conservation; gauging the symmetry removes this variance. The work thus links ETH randomness, OPE coefficient statistics, and wormhole physics to argue that global symmetries cannot exist in quantum gravity (at least in AdS contexts) unless they are gauged or broken nonperturbatively. These results provide a gravitationally rooted constraint on global symmetries and clarify how charge-sector structure in ETH manifests in holographic and gravitational frameworks.

Abstract

We generalize the eigenstate thermalization hypothesis to systems with global symmetries. We present two versions, one with microscopic charge conservation and one with exponentially suppressed violations. They agree for correlation functions of simple operators, but differ in the variance of charged one-point functions at finite temperature. We then apply these ideas to holography and to gravitational low-energy effective theories with a global symmetry. We show that Euclidean wormholes predict a non-zero variance for charged one-point functions, which is incompatible with microscopic charge conservation. This implies that global symmetries in quantum gravity must either be gauged or explicitly broken by non-perturbative effects.

Paper Structure

This paper contains 8 sections, 18 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Randomness in Holography
  3. Summary of results
  4. The ETH with global symmetries
  5. Euclidean Wormholes
  6. No Global Symmetries in Quantum Gravity
  7. Discussion
  8. Comparing ETH ansatze

Figures (1)

  • Figure 1: A genus-2 wormhole on which we compute correlation functions. On the left, the situation where the symmetry in the bulk is not gauged. This yields a non-zero correlation function. On the right, the situation where the symmetry is gauged in the bulk. In this case the field theory operators can be interpreted, using the extrapolate AdS/CFT dictionary, as the boundary limit of the bulk operator insertions which are attached to Wilson lines that end on the respective boundary. This correlation function vanishes.