Thermalization in Large-N CFTs

TL;DR

This paper investigates the thermalization behavior of multi stress tensor operators in large-N conformal field theories, demonstrating universal OPE coefficient behavior and contrasting thermalization properties of light operators.

Contribution

It provides a bootstrap proof for the universal thermalization behavior of multi stress tensor operators in large-N CFTs and verifies this through examples including holographic and free theories.

Findings

Multi stress tensor operators exhibit universal thermalization behavior.

In free CFTs, multi stress tensor operators thermalize as expected.

Light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

Abstract

In d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors. Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators. We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case. In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.