Representations of minimal W-algebras: unitarity and modular invariance.

The minimal W-algebras, obtained by quantum Hamiltonian reduction from affina vertex algebras, form the most interesting class of vertex algebras, which includes all superconformal algebras: Virasoro, Neveu-Scharz, N=2, 3, 4, and big N=4. I will explain a unified classification of their unitary representations, and their character formulas. For N=0, 1, and 2 these vertex algebras are modular invariant (meaning that tr q^L_0-c/24 is a modular function). However for all other minimal W-algebra modular invariance fails, and one needs the “modification” of characters to restore modular invariance. Unfortunately the representation-theoretical or physical meaning of the modification is not known (at least to me).

https://harvard.zoom.us/j/97784644596

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