Irregular KZ equations and Kac–Moody representations
Abstract
Abstract In this paper we construct irregular representations of the affine Kac–Moody algebra s l ^ ( 2 , C ) . We show how such irregular representations correspond to irregular Gaiotto–Teschner representations of the Virasoro algebra. The intertwiners for such representations satisfy a version of Knizhnik–Zamolodchikov (KZ) equations which we call irregular KZ equations. By connecting to 2d Liouville theory, we show how the conformal blocks governed by our irregular KZ equation correspond to 4d Argyres–Douglas theories with surface operator insertions. The corresponding flat connections describe braiding between such operators on the Gaiotto curve.
Fields of Study & Subjects
Algebraic structures and combinatorial models
Black Holes and Theoretical Physics
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Volume
- 59
- Issue
- 5
- Pages
- 055202–055202
- Publication date
- 8 January 2026