超对称杨-米尔斯理论的面向对象模拟程序
An object oriented code for simulating supersymmetric Yang--Mills theories
摘要：
超对称Yang-Mills（SYM）理论的离散化是格点场论中的一个老问题.直到最近，当从轨道结构和拓扑场论中得出的新思想被引入这个问题时，它才得到解决。其结果是创造了一类新的格点规范理论，其中格点作用量在一个或多个超对称下是不变的。由此产生的理论是本地的，免费的倍增器，也具有精确的规范不变性。原则上，它们构成了连续统SYM理论的真正非微扰定义的基础。在连续极限中，它们导致了用{ \it扭曲}场表述的杨-米尔斯理论的一个版本。在本文中，我们简要回顾了这些想法，然后继续描述的C++代码，它可以用来模拟这些理论的细节。我们简述了代码的设计，特别强调了SYM理论，其中$\mathcal{N}=2$在二维中，$\mathcal{N}=4$在三维和四维中，在SYM理论的基本组成部分与模拟中出现的相应对应部分之间进行一对一的比较
英文摘要：
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
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