[NTU String Seminar] Wilson loops in N=4 SYM from Fredholm determinants and integrable kernels

• Event Date: 2026-03-06
• Chen, Jhan Yu 陳詹喻
• High Energy Physics and Astrophysics High energy phenomenology High energy theory
• Speaker: Ludvig Chen (Uppsala University)  /  Host: Prof. Pei-Ming Ho
  Place: Rm. 815, Dept. of Physics, NTU

Title: [NTU String Seminar] Wilson loops in N=4 SYM from Fredholm determinants and integrable kernels
Speaker: Ludvig Chen (Uppsala University)
Time: 2026/3/6 (Fri.) 14:30
Place: Rm. 815, Dept. of Physics, NTU
 

Abstract

Wilson loops in higher-rank representations of N=4 SYM provide non-trivial tests of the AdS/CFT correspondence beyond the planar limit, where they are expected to be dual to D-branes in AdS_5×S^5. While Wilson loops in the antisymmetric representation are relatively well understood in the planar limit, the symmetric representation and higher-order 1/N corrections more generally remain less explored.

In this talk, I will present a new framework for studying circular half-BPS Wilson loops in the symmetric and antisymmetric representations based on Fredholm determinants with integrable Hermite kernels. Starting from the matrix model description, I will show that the generating functions for these Wilson loops can be rewritten as Fredholm determinants of integral operators whose kernels are completely integrable. This reformulation leads to a system of integro-differential equations at finite N and arbitrary ’t Hooft coupling, which can be solved using a WKB expansion, resulting in a systematic all-orders 1/N expansion.