Rationality for a Large Class of Affine W-algebras

Watch a mathematics research lecture where Robert MacRae from Tsinghua University explores strong rationality in affine W-algebras during the Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry. Delve into Huang's fundamental theorem stating that the representation category of "strongly rational" vertex operator algebras forms a semisimple modular tensor category. Examine the converse conjecture suggesting every unitary modular tensor category represents a strongly rational unitary vertex operator algebra. Learn about new findings regarding strong rationality in affine W-algebras at admissible levels, which generate modular tensor categories that extend beyond traditional affine Lie algebras at positive integer levels and Virasoro algebra associations.