arXiv 2005.036762020-05hep-thcond-mat.str-el

共形理论中的热序

Thermal Order in Conformal Theories

Noam Chai, Soumyadeep Chaudhuri, Changha Choi, Zohar Komargodski, Eliezer Rabinovici, Michael Smolkin

备注：: 66 pages, 3 figures, 3 tables, v3: matches published version
发表信息：: Phys. Rev. D 102, 065014 (2020)
DOI：: 10.1103/PhysRevD.102.065014

摘要：

人们普遍认为，在足够高的温度下，总是会失去秩序，例如磁铁失去其铁磁特性。我们提出的问题，这是否总是在$d$空间维度的量子场论的背景下的情况。更具体地说，人们可以问是否存在临界点（CFTs），在任意有限温度下打破某些全局对称性。最熟悉的CFTs在有限温度下不表现出对称性破缺，而且，在AdS/CFT对应的上下文中，有限温度下的临界点由不带电的黑膜描述，它服从无毛定理。然而，我们表明，存在的CFTs，其中有一些内部对称性打破在任意有限的温度。我们的主要例子是一个向量模型，我们研究了它的展开和任意秩以及大秩极限（和任意维数）。向量模型的大秩极限显示了有限温度下的共形流形、真空的模空间和真空的变形模空间。适当的南武-戈德斯通玻色子，包括类玻色子的确定。利用这些工具，我们建立了有限温度下有限小$ε$的对称性破缺。我们还证明了一个大类的其他不动点，其中描述了一些最常见的量子磁体，确实表现出预期的，并没有打破任何全球对称性在有限的温度。我们讨论了局部算子谱的有限温度对称性破缺的一些后果。最后，我们提出了一类不动点，这似乎是可能的候选人有限温度对称性破缺的$d=2$。

英文摘要：

It is widely expected that at sufficiently high temperatures order is always lost, e.g. magnets loose their ferromagnetic properties. We pose the question of whether this is always the case in the context of quantum field theory in $d$ space dimensions. More concretely, one can ask whether there exist critical points (CFTs) which break some global symmetry at arbitrary finite temperature. The most familiar CFTs do not exhibit symmetry breaking at finite temperature, and moreover, in the context of the AdS/CFT correspondence, critical points at finite temperature are described by an uncharged black brane which obeys a no-hair theorem. Yet, we show that there exist CFTs which have some of their internal symmetries broken at arbitrary finite temperature. Our main example is a vector model which we study both in the epsilon expansion and arbitrary rank as well as the large rank limit (and arbitrary dimension). The large rank limit of the vector model displays a conformal manifold, a moduli space of vacua, and a deformed moduli space of vacua at finite temperature. The appropriate Nambu-Goldstone bosons including the dilaton-like particle are identified. Using these tools we establish symmetry breaking at finite temperature for finite small $ε$. We also prove that a large class of other fixed points, which describe some of the most common quantum magnets, indeed behave as expected and do not break any global symmetry at finite temperature. We discuss some of the consequences of finite temperature symmetry breaking for the spectrum of local operators. Finally, we propose a class of fixed points which appear to be possible candidates for finite temperature symmetry breaking in $d=2$.

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