Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations

TL;DR

This paper proves a universal asymptotic formula for the modular S-transform of generalized partition functions in conformal field theories with higher spin currents, extending previous conjectures.

Contribution

It establishes a general, iterative method to determine the modular transformation properties of generalized Gibbs ensembles in conformal field theories.

Findings

Derived an asymptotic formula for the modular S-transform of generalized partition functions.

Proved the universality of the modular transformation properties for these ensembles.

Generalized a previous conjecture on modular properties of Gibbs ensembles.

Abstract

We study modular properties of conformal field theories perturbed by holomorphic fields. We prove an asymptotic formula for the modular S-transform of a generalized partition function that includes zero modes of higher spin holomorphic currents. The derivation makes use of general properties of torus correlation functions, in particular the Zhu recursion relation. The asymptotic expansion of the modular transformed partition function takes a universal form that is determined iteratively by the second order pole coefficients in the operator product expansion of the holomorphic currents. This proves and generalizes a conjecture regarding the modular transformation properties of generalized Gibbs ensembles.