Branes and Categorifying Integrable Lattice Models

TL;DR

This paper connects integrable lattice models to string theory brane configurations, providing a geometric and categorical framework that links 4d Chern-Simons theory, dualities, and algebraic structures like Yangians.

Contribution

It introduces a string-theoretic realization of integrable lattice models and demonstrates how to categorify key algebraic structures using brane setups and dualities.

Findings

Realization of integrable models via D-brane configurations.

Categorification of R-matrix, Yang-Baxter equation, and Yangian.

Nonperturbative integration cycle for 4d Chern-Simons theory.

Abstract

We elucidate how integrable lattice models described by Costello's 4d Chern-Simons theory can be realized via a stack of D4-branes ending on an NS5-brane in type IIA string theory, with D0-branes on the D4-brane worldvolume sourcing a meromorphic RR 1-form, and fundamental strings forming the lattice. This provides us with a nonperturbative integration cycle for the 4d Chern-Simons theory, and by applying T- and S-duality, we show how the R-matrix, the Yang-Baxter equation and the Yangian can be categorified, that is, obtained via the Hilbert space of a 6d gauge theory.