Integrable Lattice Models From Gauge Theory

TL;DR

This paper explores how integrable lattice models in statistical mechanics can be derived from four-dimensional quantum gauge theories, connecting them to known three-dimensional knot invariants and Chern-Simons theory.

Contribution

It introduces a novel framework linking integrable lattice models to four-dimensional gauge theories, expanding the understanding of their mathematical and physical foundations.

Findings

Establishes a correspondence between lattice models and 4D gauge theory

Provides insights into the relationship with Chern-Simons theory

Enhances the theoretical understanding of integrability in statistical mechanics

Abstract

These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)