On the Virasoro fusion kernel at c=25 (Ioannis Tsiares, CEA/IPhT, Paris)

31.05.2024 10:30

ABSTRACT: I will present a novel expression for the Virasoro fusion kernel in two-dimensional CFTs with central charge c=25. The expression exhibits an intricate relation with the connection coefficient of the Painlevé VI differential equation and agrees with previously known integral representations of the kernel. In the process of deriving this formula, we uncover a new symmetry in the shift relations satisfied by both the Virasoro modular and fusion kernels at generic central charge. The symmetry formally interchanges a solution valid at central charge c with another solution valid at 26 − c, much like the relation between the DOZZ formula for Liouville theory's structure constants and its ''time-like'' cousin. We will conclude by discussing a reformulation of the Virasoro bootstrap problem that incorporates the power of the Virasoro kernels, in an attempt to understand ''irrational'' 2d CFTs with c>1.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Physical Mathematics Seminar"

entrée libre