论文标题
超对称接近
Supersymmetric Proximity
论文作者
论文摘要
我认为，某些超对称性和非超对称理论之间存在某种扰动接近度（即纯Yang-mills和带有两个口味的伴随QCD，ADJQCD $ _ {n_f = 2} $）。我从$ {\ Mathcal n} = 2 $ super-yang-mills理论建立了两个$ {\ mathcal n} = 1 $ superfields：向量和手性。在$ {\ Mathcal n} = 1 $语言中，后者在su $（n）的伴随表示中呈现很重要。 $然后，我将其转换为“ {\ em phantom}”一个（类似于幽灵），打破$ {\ mathcal n} = 2 $降低到$ {\ Mathcal n} = 1 $。原始理论中两个Gluinos之间作用的全球SU（2）被分级。因此，确切的结果使变形理论允许人们在非苏格形glu差动力学的某些方面获得见解。特别是，很清楚，$β$函数系数在纯gluodynemics中的分裂是如何发生的，$β_1=（4- \ frac 13）n $和$β_2=（6- \ frac 13）n^2 $。在这里，牙套（4和6，始终整数）中的第一个术语与几何相关，而第二个术语（两种情况下$ - \ frac 13 $）是{\ it bona fide}量子效应。从同样的意义上讲，ADJQCD $ _ {n_f = 2} $接近$ {\ Mathcal n} = 2 $ sym。 因此，我在纯gluodynemics和Adjqcd $ _ {n_f = 2} $之间建立了一定的接近性，并具有超对称理论。 （当然，在这两种情况下，我们都会散发与平面方向和higgs/coulomb分支相关的所有功能，$ {\ Mathcal n} = 2 $。）作为热身练习，我在2D CP（1）Sigma模型中使用$ {\ MATHCAL N} =（2,2）$ SUPESMYMMETRY的$ {\ Mathcal n} =（2,2） \至$ bosonic CP（1）。
I argue that a certain perturbative proximity exists between some supersymmetric and non-supersymmetric theories (namely, pure Yang-Mills and adjoint QCD with two flavors, adjQCD$_{N_f=2}$). I start with ${\mathcal N}=2$ super-Yang-Mills theory built of two ${\mathcal N}=1$ superfields: vector and chiral. In ${\mathcal N}=1$ language the latter presents matter in the adjoint representation of SU$(N). $ Then I convert the matter superfield into a "{\em phantom}" one (in analogy with ghosts), breaking ${\mathcal N}=2$ down to ${\mathcal N}=1$. The global SU(2) acting between two gluinos in the original theory becomes graded. Exact results in thus deformed theory allows one to obtain insights in certain aspects of non-supersymmetric gluodynamics. In particular, it becomes clear how the splitting of the $β$ function coefficients in pure gluodynamics, $β_1 =(4 -\frac 13 )N$ and $β_2= (6-\frac 13)N^2$, occurs. Here the first terms in the braces (4 and 6, always integers) are geometry-related while the second terms ($-\frac 13$ in both cases) are {\it bona fide} quantum effects. In the same sense adjQCD$_{N_f=2}$ is close to ${\mathcal N}=2$ SYM. Thus, I establish a certain proximity between pure gluodynamics and adjQCD$_{N_f=2}$ with supersymmetric theories. (Of course, in both cases we loose all features related to flat directions and Higgs/Coulomb branches in ${\mathcal N}=2$.) As a warmup exercise I use this idea in 2D CP(1) sigma model with ${\mathcal N}=(2,2)$ supersymmetry, through the minimal heterotic ${\mathcal N}=(0,2) \to$ bosonic CP(1).
