Supersymmetric Yang--Mills theories with exact supersymmetry on the lattice

TL;DR

This paper reviews the construction of maximally twisted supersymmetric Yang--Mills theories on the lattice, enabling exact supersymmetry preservation and facilitating studies of strongly coupled regimes and dual gravitational theories.

Contribution

It discusses the formulation of lattice SYM theories with exact supersymmetry using topological twisting and explores their applications in non-perturbative and thermal analyses.

Findings

One-loop renormalization of 4D ${\cal N}=4$ SYM on the lattice.

Construction of lattice theories preserving exact supersymmetry.

Applications in studying thermal phases and dual gravitational properties.

Abstract

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang--Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean spacetime lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice ${\cal N}=4$ SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.