An object oriented code for simulating supersymmetric Yang--Mills theories

TL;DR

This paper introduces a C++ simulation code for supersymmetric Yang--Mills theories on the lattice, leveraging recent advances that preserve some supersymmetry and gauge invariance, enabling non-perturbative studies.

Contribution

It provides a detailed design and implementation of a C++ code for simulating lattice supersymmetric Yang--Mills theories with exact supersymmetry and gauge invariance.

Findings

Code successfully simulates 2D and 4D SYM theories

Preserves supersymmetry and gauge invariance on the lattice

Enables non-perturbative analysis of SYM theories

Abstract

Discretization of supersymmetric Yang--Mills (SYM) theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they lead to a version of the Yang-Mills theory formulated in terms of {\it twisted} fields. In this paper, we briefly review these ideas and then go on to describe the details of a C++ code, which can be used to simulate these theories. We sketch the design of the code, with particular emphasis being placed on SYM theories with $\mathcal{N}=2$ in two dimensions and $\mathcal{N}=4$ in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation