Coarse-graining in time, emergent temperature in 2d CFT at large central charge

TL;DR

This paper derives a compact expression for two-point functions in large-$c$ 2d CFTs, showing how coarse-graining over time leads to emergent thermal behavior and state projection consistent with bootstrap results.

Contribution

It introduces a monodromy method-based compact formula for expectation values in time-dependent states and reveals how coarse-graining induces thermalization and state projection.

Findings

Thermal two-point functions emerge above a coarse-graining time-scale.

Pure states appear projected onto a single conformal representation.

Results align with known conformal bootstrap findings.

Abstract

Using the monodromy method, a compact expression is obtained for the identity block contribution to the expectation value of two low-energy probe operators on a broad class of time-dependent heavy pure states in large-$c$ 2d CFTs. It will be shown that the size of the compact spatial dimension sets a coarse-graining time-scale above which the thermal two-point function naturally emerges. A phenomena will be highlighted where the information of the pure state appears to get projected down to a single conformal representation. We will see that this projection is corroborated by known conformal bootstrap results.