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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 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 |
