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.
Highlights
The thermal behavior of quantum many-body systems is well understood in terms of statistical mechanics
In this Letter, we will discuss how global symmetries interact with the eigenstate thermalization hypothesis (ETH), wormholes and erratic signals of quantum chaos
We discuss two possible variants of a charged ETH, one that preserves the symmetry microscopically, the other that allows for exponentially small violations of charge conservation in the random variables
Summary
The thermal behavior of quantum many-body systems is well understood in terms of statistical mechanics. For the purpose of computing few-point correlation functions of simple operators in high energy states, these microscopic details are irrelevant and it suffices to treat the Ri j as true random variables. This randomness is tightly linked to the connection between quantum chaotic systems and random matrix theory (see [3] for a review). New insights into the randomness of chaotic quantum systems have emerged from gravitational physics, through holographic duality [4]. Quantum thermalization has been discussed in the context of holography for precisely this reason (see for example [9,10,11,12,13,14,15,16,17,18,19,20])
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have