Towards a Modular Bootstrap of Non-Rational Virasoro CFTs

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 ⋊ SN.
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 ⋊ SN 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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