Towards a Modular Bootstrap of Non-Rational Virasoro CFTs

par Maddalena Ferragatta (CPhT, École polytechnique)

mercredi 27 mai 2026, 10:30 → 11:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

Spring '26: TQFT and Knot Theory 

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 Fib^⊠N ⋊ 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 Fib^⊠N ⋊ 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.

More information: https://seedseminar.apps.math.cnrs.fr/program/#may-27-2026

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