An object oriented code for simulating supersymmetric Yang--Mills 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

30 pages, 8 figures. Minor edits. Published version Computer Physics Communications 183 (2012), 1336-1353

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• N=4 Supersymmetry on a Space-Time Lattice
• Parallel software for lattice N=4 supersymmetric Yang--Mills theory
• Phase Structure of Lattice N=4 Super Yang-Mills
• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Investigating the sign problem for two-dimensional $\mathcal{N}=(2,2)$ and $\mathcal{N}=(8,8)$ lattice super Yang--Mills theories
• Lattice formulation of two-dimensional N=(2,2) super Yang-Mills with SU(N) gauge group
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• Lattice Formulation of $\mathcal{N}=2^{\ast }$ Yang-Mills
• Spontaneous supersymmetry breaking in two dimensional lattice super QCD
• $\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice