“Lattice Yang-Mills theory in the large N limit via sums over surfaces”
Lunedì 5 Maggio 2025, ore 14:30 - Aula 1BC45 - Jacopo Borga (Massachusetts Institute of Technology - MIT)
Abstract
Lattice Yang-Mills theories are important models in particle physics. They are defined on the d-dimensional lattice Z^d using a group of matrices of dimension N, and Wilson loop expectations are the fundamental observables of these theories. Recently, Cao, Park, and Sheffield showed that Wilson loop expectations can be expressed as sums over certain embedded bipartite maps of any genus. Building on this novel approach, we prove in the so-called strongly coupled regime:
- A rigorous formula in terms of embedded bipartite planar maps of Wilson loop expectations in the large N limit, in any dimension d.
- An exact computation of Wilson loop expectations in the large N limit, in dimension d=2, for a large family of (simple and non-simple) loops.
Previous results to the two aforementioned points were established by Chatterjee (2019) and Basu & Ganguly (2016), respectively. Our results extend these previous results, offer simpler proofs and provide a new perspective on these significant quantities.
This work is a collaboration with Sky Cao and Jasper Shogren-Knaak.
Seminars in Probability and Finance
