Random Field Ising Model and Parisi-Sourlas supersymmetry. Part I. Supersymmetric CFT
Random Field Ising Model and Parisi-Sourlas supersymmetry. Part I. Supersymmetric CFT
复制标题
随机场 Ising 模型和 Parisi-Sourlas 超对称性。
DOI：
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发表时间：
2019
影响因子：
5.4
通讯作者：
Emilio Trevisani
中科院分区：
文献类型：
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作者：
A. Kaviraj;S. Rychkov;Emilio Trevisani
淬灭无序非常重要，但众所周知很难。1979年，Parisi和Sourlas提出了一个关于具有随机场型无序的红外不动点的有趣而有力的猜想：这样的不动点应该具有不寻常的超对称性，通过这种超对称性，它们在两个较小的空间维度上减少到通常的非超对称非无序不动点。然而，这个猜想在一些简单的情况下是失败的，但是对于为什么会发生这种情况还没有达成共识。在本文中，我们给出了新的非微扰参数的降维。我们用共形场论（CFT）的语言重新描述这个问题。然后，我们展示了从d维Parisi-Sourlas超对称CFT到（d − 2）维普通CFT的算子和相关函数的映射。约化理论是局部的，即它有一个局部守恒的应力张量算子。由于需要减少，我们表现出一个完美的匹配之间的超共形块和通常的共形块在两个维度较低。这也导致了一个新的关系，共形块跨尺寸。本文关注的第二个一半的巴黎-Sourlas猜想，而第一个一半（存在一个超对称不动点）将审查在同伴的工作。
Quenched disorder is very important but notoriously hard. In 1979, Parisi and Sourlas proposed an interesting and powerful conjecture about the infrared fixed points with random field type of disorder: such fixed points should possess an unusual supersymmetry, by which they reduce in two less spatial dimensions to usual non-supersymmetric non- disordered fixed points. This conjecture however is known to fail in some simple cases, but there is no consensus on why this happens. In this paper we give new non-perturbative arguments for dimensional reduction. We recast the problem in the language of Conformal Field Theory (CFT). We then exhibit a map of operators and correlation functions from Parisi-Sourlas supersymmetric CFT in d dimensions to a (d − 2)-dimensional ordinary CFT. The reduced theory is local, i.e. it has a local conserved stress tensor operator. As required by reduction, we show a perfect match between superconformal blocks and the usual conformal blocks in two dimensions lower. This also leads to a new relation between conformal blocks across dimensions. This paper concerns the second half of the Parisi-Sourlas conjecture, while the first half (existence of a supersymmetric fixed point) will be examined in a companion work.