Generalized Gibbs Ensemble of 2d CFTs at large central charge in the thermodynamic limit

TL;DR

This paper computes the generalized partition function of 2d conformal field theories with higher qKdV charges at large central charge in the thermodynamic limit, revealing exact results and finite-c corrections.

Contribution

It provides explicit calculations of the generalized partition function and 1/c corrections, and compares ensemble equivalences at infinite and large but finite central charge.

Findings

Exact generalized partition function at infinite central charge.

Finite-c corrections expressed as sums over Young tableaux.

Discrepancies between ensembles at finite central charge.

Abstract

We discuss partition function of 2d CFTs decorated by higher qKdV charges in the thermodynamic limit when the size of the spatial circle goes to infinity. In this limit the saddle point approximation is exact and at infinite central charge generalized partition function can be calculated explicitly. We show that leading 1/c corrections to free energy can be reformulated as a sum over Young tableaux which we calculate for the first two qKdV charges. Next, we compare generalized ensemble with the "eigenstate ensemble" that consists of a single primary state. At infinite central charge the ensembles match at the level of expectation values of local operators for any values of qKdV fugacities. When the central charge is large but finite, for any values of the fugacities the aforementioned ensembles are distinguishable.