Probability seminar

September 11, 2025: Ron Nissim (MIT) (**AP&M 7321**)
Title: Area Law for Lattice Yang-Mills at Strong Coupling
Abstract: This talk is based on joint work with Scott Sheffield and Sky Cao on lattice Yang-Mills theory. Yang-Mills theory is the mathematical model for the standard model of particle physics, and the area law is the property of the Yang-Mills model said to explain the physical phenomenon of quark confinement. The lattice Yang-Mills model assigns a random NxN matrix from classical Lie groups such as U(N), SU(N), or SO(N) to each edge of a lattice. An adjustable parameter of the model, beta, sometimes referred to as "inverse temperature" describes the coupling strength of the model. It is generally believed that the lattice Yang-Mills model greatly simplifies when beta is proportional to N and N gets large, and in the N->infinity limit under this scaling, area law is known to hold. Nevertheless, for finite N the area law was only shown for beta < c_d/N for a dimensional constant c_d prior to our work (a regime of beta which gets smaller as N gets large!). In a recent preprint we use a novel surface exploration point of view to increase the range of parameters to beta < c_d independent of N, and in ongoing work we use the dynamical perspective introduced by Shen, Zhu, and Zhu to further improve the regime to  beta < c_d N which is the scaling of the previously mentioned large N limit of the model. Both of these approaches work for any dimension of the lattice, d. Introducing these two approaches to the area law question will be the goal of the talk.

Previous seminar talks from 2024-2025 are found here