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An object oriented code for simulating supersymmetric Yang-Mills theories

机译：模拟超对称Yang-Mills理论的面向对象代码

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摘要

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.
机译：我们介绍SUSY-LATTICE-一种C ++程序，可用于在平坦的欧几里得时空网格上模拟某些类的超对称Yang-Mills（SYM）理论，包括四个维度的著名N = 4 SYM。 SYM理论的离散化是晶格场理论中的一个老问题。直到最近，当人们从双向结构和拓扑场论中汲取新思想时，它一直拒绝解决。结果就是创建了新的一类晶格规范理论，其中晶格作用在一个或多个超对称下是不变的。所得理论是局部的，没有倍增器，并且也具有精确的规范不变性。原则上，它们构成了连续统SYM理论的真正非扰动定义的基础。在连续极限中，它们再现了以扭曲场表示的SYM理论的版本，这在平坦的时空只是场变量的变化。在本文中，我们简要回顾了这些想法，然后继续提供C ++代码的详细信息。我们对代码的设计进行了概述，特别着重于SYM理论，其中二维的N =（2,2），三维的N = 4，四个维度，一对一比较。 SYM理论及其对应的对等物出现在仿真代码中。该代码可用于计算与SYM理论相关的多个量，例如Polyakov环，平均能量和标量特征值分布的宽度。

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