Lattice Studies of Two-Dimensional Maximally Supersymmetric Yang-Mills Theory for Tests of Gauge-Gravity Duality

TL;DR

This paper develops lattice formulations of 2D maximally supersymmetric Yang-Mills theory to enable numerical tests of gauge-gravity duality and explore non-perturbative aspects.

Contribution

It constructs lattice actions preserving some supersymmetry and extends software for simulations, aiding non-perturbative studies of supersymmetric gauge theories.

Findings

Lattice actions preserving a subset of supersymmetries are constructed.

Software routines are extended for lower-dimensional supersymmetric theories.

Simulations enable exploration of the continuum limit and gauge-gravity duality tests.

Abstract

We present our ongoing work on two-dimensional maximally supersymmetric Yang-Mills (2D MSYM) theory using lattice techniques. The continuum theory is obtained from the dimensional reduction of four-dimensional ${\mathcal N} = 4$ supersymmetric Yang-Mills theory. We construct both the continuum and lattice versions of the 2D MSYM theory. The lattice action preserves a subset of supersymmetries. We extend existing lattice software with new routines to accommodate the additional terms in the lower-dimensional theory. This lattice construction enables us to perform Rational Hybrid Monte Carlo simulations of 2D MSYM and facilitates the exploration of its continuum limit. Our work contributes to the numerical study of maximally supersymmetric gauge theories and supports the ongoing efforts to test gauge-gravity duality and investigate related non-perturbative phenomena.