Supersymmetric Lattice Theories: Contribution to Snowmass 2022

TL;DR

This paper reviews the development of lattice theories with exact supersymmetry, especially N=4 Yang-Mills, enabling non-perturbative studies relevant to quantum gravity and conformal field theories.

Contribution

It summarizes the construction and applications of supersymmetric lattice theories, highlighting their role in non-perturbative physics and holography.

Findings

Lattice formulations allow numerical simulations of N=4 Yang-Mills at strong coupling.

These simulations provide insights into non-perturbative aspects of quantum gravity.

The work advances understanding of holographic dualities and conformal field theories.

Abstract

In this white paper we summarise the construction and applications of lattice theories possessing exact supersymmetry focusing, in particular, on N=4 Yang-Mills theory. Lattice formulations of this theory allow for numerical simulation of the theory at strong coupling and hence give a window on non-perturbative physics away from the planar limit. This has important applications to our understanding of holographic approaches to quantum gravity and conformal field theories.