Modular transform of free fermion generalised Gibbs ensembles and generalised power partitions

TL;DR

This paper extends the understanding of modular transformations in free fermion GGEs by generalizing conjectures to multiple KdV charges and connecting these to power partitions, with proofs for finite cases.

Contribution

It generalizes the modular transformation conjecture for free fermion GGEs to include multiple KdV charges and relates these to generalized power partitions.

Findings

Proved the modular transformation for finite KdV charges in GGEs.

Extended the conjecture to infinite KdV charges case.

Connected GGEs to generalized power partitions.

Abstract

In [1] a conjecture for the modular transformation of the free fermion generalised Gibbs ensemble (GGE) was given where only the KdV charge associated to the weight four quasi primary field was inserted. In this paper we first generalise this conjecture to the case with an arbitrary, finite collection of KdV charges in the GGE. These GGEs are generalisations of the generating function of power partitions. We prove the conjectured transformation for the case with a finite number of charges inserted and discuss the case with an infinite number of charges.