Ludvig Chen: Fredholm determinants, differential equations and matrix models

Wednesday 18 Feb 2026, 13:30 → 14:30 Europe/Stockholm

Å92110 (Ångströmslaboratoriet)

Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with integrable kernels. This classical result has recently been used compute various observables in different four-dimensional superconformal Yang-Mills theories as Fredholm determinants. These Fredholm determinants with a kernel of integrable form can in turn be mapped to a system of differential equations.

In this talk, I will present the underlying framework of this machinery and describe how Fredholm determinants and integrable kernels naturally arise from the matrix model description of higher-rank Wilson loops in N = 4 SYM. I will show that the associated differential equations admit a WKB expansion, leading to a systematic all-orders 1/N expansion of higher-rank Wilson loops in the symmetric and antisymmetric representations of SU(N).

This talk is based on upcoming work with V. Mishnyakov and K. Zarembo.