论文标题
随机字段$ ϕ^3 $型号和巴黎 - 苏拉斯超对称性
Random Field $ϕ^3$ Model and Parisi-Sourlas Supersymmetry
论文作者
论文摘要
我们使用ARXIV：2009.10087中设置的RG框架来探索具有随机场相互作用的$ ϕ^3 $理论。根据巴黎 - 苏拉斯（Parisi-Sourlas）的猜想，该理论接受了一个固定点，其出现的超对称性与纯Lee-Yang CFT相关，这两个较小的维度。我们使用$ d = 8-ε$的副本技巧和CARDY变量研究该模型，其中RG流动为扰动。允许的扰动是$ s_n $对称性下的单元，该单元列入了$ n $ epplicas。这些分解为具有不同尺度的操作员：最低的尺寸部分“领导者”控制IR中的RG流动；其他运营商“追随者”可以忽略。领导者根据他们的混合特性，将领导者分为以下方式：Susy-worlable，Susy-Null和非令人敬畏的事物。我们构建了低谎言的领导者，并计算了许多领导者的异常维度。我们认为，没有运营商可以破坏$ d \ le 8 $中的Susy RG流动。这与分支聚合物的关键指数（与随机字段$ ϕ^3 $模型相同的普遍性类别）的关键指数的众所周知的数值结果一致，该指数符合纯Lee-Yang固定点的尺寸减小，所有$ 2 \ le d \ le d \ le 8 $。因此，这是对RG框架的第二次强制检查，该框架以前被证明可以正确预测随机场ISING模型中尺寸降低的损失。
We use the RG framework set up in arXiv:2009.10087 to explore the $ϕ^3$ theory with a random field interaction. According to the Parisi-Sourlas conjecture this theory admits a fixed point with emergent supersymmetry which is related to the pure Lee-Yang CFT in two less dimensions. We study the model using replica trick and Cardy variables in $d=8-ε$ where the RG flow is perturbative. Allowed perturbations are singlets under the $S_n$ symmetry that permutes the $n$ replicas. These are decomposed into operators with different scaling dimensions: the lowest dimensional part, `leader', controls the RG flow in the IR; the other operators, `followers', can be neglected. The leaders are classified into: susy-writable, susy-null and non-susy-writable according to their mixing properties. We construct low lying leaders and compute the anomalous dimensions of a number of them. We argue that there is no operator that can destabilize the SUSY RG flow in $d\le 8$. This agrees with the well known numerical result for critical exponents of Branched Polymers (which are in the same universality class as the random field $ϕ^3$ model) that match the ones of the pure Lee-Yang fixed point according to dimensional reduction in all $2\le d\le 8$. Hence this is a second strong check of the RG framework that was previously shown to correctly predict loss of dimensional reduction in random field Ising model.
