An object oriented code for simulating supersymmetric Yang–Mills theories

Abstract

We present SUSY_LATTICE – a C++ program that can be used to simulate certain classes of supersymmetric Yang–Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space–time lattice. Discretization of 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 reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space–time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and 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 code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICECatalogue identifier: AELS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9315No. of bytes in distributed program, including test data, etc.: 95 371Distribution format: tar.gzProgramming language: C++Computer: PCs and WorkstationsOperating system: Any, tested on Linux machinesClassification:: 11.6Nature of problem: To compute some of the observables of supersymmetric Yang–Mills theories such as supersymmetric action, Polyakov/Wilson loops, scalar eigenvalues and Pfaffian phases.Solution method: We use the Rational Hybrid Monte Carlo algorithm followed by a Leapfrog evolution and a Metropolis test. The input parameters of the model are read in from a parameter file.Restrictions: This code applies only to supersymmetric gauge theories with extended supersymmetry, which undergo the process of maximal twisting. (See Section 2 of the manuscript for details.)Running time: From a few minutes to several hours depending on the amount of statistics needed.