Integrable 3D lattice model in M-theory

TL;DR

This paper proposes a connection between M-theory brane systems and integrable 3D lattice models, showing that their supersymmetric index equals the partition function of such models, with weights satisfying generalized tetrahedron equations.

Contribution

It establishes a novel link between M-theory brane indices and integrable lattice models, extending the understanding of their mathematical structure.

Findings

Supersymmetric index equals lattice model partition function

Local weights satisfy generalized tetrahedron equations

Special case relates to known tetrahedron solutions

Abstract

It is argued that the supersymmetric index of a certain system of branes in M-theory is equal to the partition function of an integrable three-dimensional lattice model. The local Boltzmann weights of the lattice model satisfy a generalization of Zamolodchikov's tetrahedron equation. In a special case the model is described by a solution of the tetrahedron equation discovered by Kapranov and Voevodsky and by Bazhanov and Sergeev.