Characters of the Virasoro algebra and Kac-Moody algebras have good modular transformation properties. It is an open question whether characters of W-algebras have such properties. As a tractable test case, we look at generalised Gibbs ensembles for the KdV charges for a free fermion, which we expect to share many of the same properties. We show that such traces cannot close under modular transformations and we conjecture an expression for the modular transform involving an altered set of modes. We suggest a simple interpretation for this result.

King’s College, London