Universal Modular Properties of Generalized Gibbs Ensembles and Chiral Deformations

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. We have also found an explicit expression for the multiplicities of terms generated by the iteration. This proves and generalizes a conjecture regarding the modular transformation properties of generalized Gibbs ensembles.