Heavy Operators and Hydrodynamic Tails

TL;DR

This paper demonstrates how hydrodynamics universally determines the average OPE coefficients involving heavy and light operators in conformal field theories, extending previous EFT results and analyzing late-time thermal correlators.

Contribution

It introduces a universal hydrodynamic approach to fix OPE coefficients for heavy-light operators in CFTs, generalizing recent EFT findings and applicable to theories with global symmetries.

Findings

Hydrodynamics fixes average OPE coefficients for heavy-light operators.

Extension of methods to CFTs with global symmetries.

Revisiting late-time thermal correlators in QFT and diffusive systems.

Abstract

The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators -- which are generically expected to create thermal states -- can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients $C_{HH'L}$, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. We also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems.