Classical conformal blocks, Coulomb gas integrals, and quantum integrable models

TL;DR

This paper explores the connection between classical conformal blocks, Coulomb gas integrals, and quantum integrable models, introducing a new method for calculating classical conformal blocks using saddle-point limits.

Contribution

It presents a novel approach to compute classical conformal blocks via Coulomb gas integrals and saddle-point analysis, linking conformal field theory with quantum integrable models.

Findings

Identified saddle-point limit as the classical limit of conformal blocks

Developed a new method for calculating classical conformal blocks

Connected Coulomb gas integrals with quantum integrable models

Abstract

In this paper, we recall Richardson's solution of the reduced BCS model, its relationship with the Gaudin model, and the known implementation of these models in conformal field theory. The CFT techniques applied here are based on the use of the free field realization, or more precisely, on the calculation of saddle-point values of Coulomb gas integrals representing certain (perturbed) WZW conformal blocks. We identify the saddle-point limit as the classical limit of conformal blocks. We show that this observation implies a new method for calculating classical conformal blocks and can be further used in the study of quantum integrable models.