Lattice formulations of supersymmetric gauge theories with matter fields

TL;DR

This paper reviews recent developments in formulating supersymmetric gauge theories with matter fields on Euclidean lattices, emphasizing techniques that preserve supersymmetry and gauge invariance.

Contribution

It introduces new lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields, maintaining exact supersymmetry and gauge invariance.

Findings

Lattice formulations preserve exact supersymmetry.

Gauge invariance and locality are maintained.

Successful discretizations of supersymmetric theories with matter fields.

Abstract

Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.