Virasoro Conformal Blocks and Thermality from Classical Background Fields

TL;DR

This paper demonstrates that in large central charge 2d CFTs, heavy operator effects can be incorporated via a background metric, refining Virasoro conformal blocks and shedding light on black hole thermality and eigenstate thermalization.

Contribution

It introduces a method to compute Virasoro blocks by absorbing stress tensor couplings into a background metric, extending to charged operators and deriving a new recursion relation.

Findings

Virasoro blocks are equivalent to global blocks in a modified background.

The method applies to operators with U(1) charges.

Implications for black hole thermality and eigenstate thermalization in AdS3/CFT2.

Abstract

We show that in 2d CFTs at large central charge, the coupling of the stress tensor to heavy operators can be re-absorbed by placing the CFT in a non-trivial background metric. This leads to a more precise computation of the Virasoro conformal blocks between heavy and light operators, which are shown to be equivalent to global conformal blocks evaluated in the new background. We also generalize to the case where the operators carry U(1) charges. The refined Virasoro blocks can be used as the seed for a new Virasoro block recursion relation expanded in the heavy-light limit. We comment on the implications of our results for the universality of black hole thermality in $AdS_3$, or equivalently, the eigenstate thermalization hypothesis for $CFT_2$ at large central charge.