I argue that a certain perturbative proximity exists between some supersymmetric and nonsupersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, adjQCDNf=2). I start with N=2 super–Yang-Mills theory built of two N=1 superfields: vector and chiral. In N=1 language, the latter presents matter in the adjoint representation of SU(N). Then, I convert the matter superfield into a phantom one (in analogy with ghosts), breaking N=2 down to N=1. The global SU(2) acting between two gluinos in the original theory becomes graded. Exact results in thus deformed theory allow one to obtain insights in certain aspects of nonsupersymmetric gluodynamics. In particular, it becomes clear how the splitting of the β function coefficients in pure gluodynamics, β1=(4-13)N and β2=(6-13)N2, occurs. Here, the first terms in the braces (4 and 6, always integers) are geometry related, while the second terms (-13 in both cases) are bona fide quantum effects. In the same sense, adjQCDNf=2 is close to N=2 SYM. Thus, I establish a certain proximity between pure gluodynamics and adjQCDNf=2 with supersymmetric theories. (Of course, in both cases, we loose all features related to flat directions and Higgs/Coulomb branches in N=2.) As a warmup exercise, I use this idea in the two-dimensional CP(1) sigma model with N=(2,2) supersymmetry, through the minimal heterotic N=(0,2)→ bosonic CP(1).

中文翻译：

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超对称和非超对称理论之间的微扰接近度

我认为在一些超对称和非超对称理论（即纯杨-米尔斯和具有两种风格的伴随 QCD，adjQCDNf=2）之间存在某种微扰接近。我从 N=2 超杨米尔斯理论开始，该理论由两个 N=1 超场构成：矢量和手性。在 N=1 语言中，后者在 SU(N) 的伴随表示中呈现物质。然后，我将物质超场转换为幻影超场（类似于鬼），将 N=2 分解为 N=1。原始理论中作用于两个 gluinos 之间的全局 SU(2) 变得分级。如此变形的理论中的精确结果使人们能够深入了解非超对称胶体动力学的某些方面。特别是，很清楚纯胶动力学中 β 函数系数的分裂是如何发生的，β1=(4-13)N 和 β2=(6-13)N2。这里，大括号中的第一项（4 和 6，总是整数）是几何相关的，而第二项（在两种情况下都是-13）是真正的量子效应。同理，adjQCDNf=2 接近于 N=2 SYM。因此，我用超对称理论在纯胶动力学和 adjQCDNf=2 之间建立了一定的接近度。（当然，在这两种情况下，我们都在 N=2 中丢失了与平面方向和 Higgs/Coulomb 分支相关的所有特征。）作为热身练习，我在二维 CP(1) sigma 模型中使用了这个想法，其中 N= (2,2) 超对称，通过最小杂优势 N=(0,2)→ 玻色 CP(1)。