Current trimester: TQFT and Knot Theory
The kickoff event took place at IHP on 22.04.2026 (https://indico.math.cnrs.fr/event/16226/)
Towards a modular bootstrap of non-rational Virasoro CFTs
byMaddalena Ferragatta
Abstract:Non-rational 2d CFTs are defined as unitary CFTs with \(c>1\), a normalizable vacuum, a discrete spectrum, a modular invariant torus partition function, and no conserved currents beside those of the Virasoro identity module.
Perturbative results and lattice simulations suggest that a large class of these non-rational CFTs can be engineered as critical points of RG flows that couple N copies of unitary Virasoro minimal models, while preserving a non-invertible categorical symmetry of the form \(\text{Fib}^{\boxtimes N}\rtimes S_N\).
In this talk I will give a pedagogical introduction to fusion categories and their tube algebra representations in terms of defect lines. I will then discuss how to extend the modular conformal bootstrap approach to study 2d CFTs with \(\text{Fib}^{\boxtimes N}\rtimes S_N\) non-invertible categorical symmetry and present some preliminary numerical results for this analysis.
Based on 2602.06117 with Balt van Rees and a WIP with Junchen Rong, Francesco Russo and Balt van Rees.