Classical conformal blocks, blow-up equations and periodic spectral problems (Tommaso PEDRONI, SISSA)

15.05.2025 11:00

Abstract:
In this talk, we will examine the correspondences between 4d N=2 supersymmetric gauge theories, 2d conformal field theory and quantum integrable systems.
In particular, we will address the difficulties in applying the Nekrasov-Shatashvili (NS) quantization scheme to quantum integrable systems with periodic potentials, focusing on the simplest elliptic case.
Starting from two-point torus conformal blocks with a degenerate insertion, I will analyze their monodromy properties and show how the classical limit of the BPZ equation leads to the Lamé equation and its connection formulas.
I will then examine the analytic structure of classical conformal blocks, showing how apparent poles become branch points through a partial resummation obtained by solving a specific limit of the C^{2}/Z_{2} blow-up equations.
Finally, we will study the periodic spectral problems associated with the Lamé equation using this newly acquired information about classical conformal blocks.

Lieu

Conseil Général 7-9, Salle 1-15, Séminaire Physique Mathématique

entrée libre