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Résumé |
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. 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. |
