We study the modular properties of the torus partition functions of 2d CFTs in the case where the Hamiltonian is perturbed by the zero mode of a holomorphic field. Concrete computations involving Generalised Gibbs ensembles (GGE) associated to the (integrable) Boussinesq hierarchy suggests that the modular S-transforms of symmetrised n-point functions of the charges of the hierarchy take a simple form. Based on this observation, we conjecture a general formula for the asymptotic expansion (in the fugacities) for the S-transformed generalised characters in a rational CFT. Assuming certain properties for the S-transform, we also provide a derivation for this formula. The talk will be based on 2508.16258 [hep-th] and 2603.28244 [hep-th].
ZoomMeeting: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
Passcode: 232322