[Paper Review] Charged Eigenstate Thermalization, Euclidean Wormholes and Global Symmetries in Quantum Gravity

Alexandre Belin, Jan de Boer+2 more|arXiv (Cornell University)|Dec 14, 2020

Black Holes and Theoretical Physics4 citations

TL;DR

This paper generalizes the Eigenstate Thermalization Hypothesis (ETH) to quantum systems with global symmetries, introducing two variants: one with exact charge conservation and one with exponentially suppressed violations. It shows that Euclidean wormholes in quantum gravity predict a non-zero variance in charged one-point functions, which contradicts microscopic charge conservation—implying global symmetries in quantum gravity must be either gauged or explicitly broken by non-perturbative effects.

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.

Motivation & Objective

• To extend the Eigenstate Thermalization Hypothesis (ETH) to systems with global U(1) symmetries.
• To investigate how charged operators behave in thermal states when global symmetries are present.
• To determine whether Euclidean wormholes in quantum gravity are compatible with exact global symmetries.
• To clarify the distinction between microscopic charge conservation and effective theories with small violations.
• To establish a connection between gravitational path integral contributions and statistical properties of CFT OPE coefficients.

Proposed method

• Proposes two versions of ETH: one preserving global symmetry microscopically, the other allowing exponentially small violations.
• Uses random matrix theory and statistical averaging to model chaotic quantum systems with conserved charge.
• Analyzes two-point functions of charged operators in the microcanonical ensemble to compare predictions of the two ETH variants.
• Applies the framework to holographic CFTs and low-energy effective gravity, linking ETH to gravitational path integrals.
• Evaluates the role of Euclidean wormholes in generating non-zero variance in charged one-point functions.
• Compares the two ETH ansätze via integrals over energy and charge differences, showing agreement for low-point functions but divergence in higher moments.

Experimental results

Research questions

• RQ1 How does the Eigenstate Thermalization Hypothesis generalize in the presence of global U(1) symmetries?
• RQ2 What is the physical distinction between a global symmetry that is conserved microscopically versus one with exponentially small violations?
• RQ3 Can Euclidean wormholes in quantum gravity coexist with exact global symmetries?
• RQ4 How do charged one-point functions behave in the presence of wormhole contributions, and what does this imply for symmetry realization?
• RQ5 What constraints do gravitational path integral computations place on the statistical structure of OPE coefficients in CFTs?

Key findings

• The two ETH variants—microscopic charge conservation vs. exponentially suppressed violations—yield identical predictions for low-point correlation functions of simple operators.
• The variants differ significantly in the variance of charged one-point functions at finite temperature, with the non-conserving version predicting a non-zero variance.
• Euclidean wormholes in the gravitational path integral predict a non-zero variance for charged one-point functions, which contradicts exact charge conservation.
• This contradiction implies that global symmetries in quantum gravity cannot be fundamental; they must be either gauged or explicitly broken by non-perturbative effects.
• The results support the idea that the low-energy effective theory of quantum gravity encodes statistical properties of CFT data, such as OPE coefficients, through gravitational path integral contributions.
• The framework connects holographic chaos, random matrix theory, and the structure of black hole microstates via a statistical description of OPE coefficients.