TY - JOUR

T1 - An object oriented code for simulating supersymmetric Yang-Mills theories

AU - Catterall, Simon

AU - Joseph, Anosh

N1 - Funding Information:
This work is supported in part by DOE under grant number DE-FG02-85ER40237 . Simulations were performed using USQCD resources at Fermilab. We would like to thank useful discussions with Richard Galvez, Joel Giedt, Dhagash Mehta and Greg van Anders.

PY - 2012/6

Y1 - 2012/6

N2 - 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.

AB - 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.

KW - Lattice gauge theory

KW - Object oriented programming

KW - Rational hybrid Monte Carlo

KW - Supersymmetric Yang-Mills

UR - http://www.scopus.com/inward/record.url?scp=84857784280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857784280&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2012.01.024

DO - 10.1016/j.cpc.2012.01.024

M3 - Article

AN - SCOPUS:84857784280

SN - 0010-4655

VL - 183

SP - 1336

EP - 1353

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 6

ER -