Geometries from field theories
Geometries from field theories
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场论中的几何
DOI：
10.1093/ptep/ptv131
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发表时间：
2015
影响因子：
3.5
通讯作者：
K. Kikuch and T. Onogi
中科院分区：
文献类型：
--
作者：
S. Aoki;K. Kikuch and T. Onogi
本文提出了一种从一维量子场论的展开式定义一维几何的方法。我们首先从一维场论出发，通过梯度流方程构造了一维场论，其流动时间代表了系统的能量尺度，对应于紫外和红外。然后，我们定义诱导度量从维场算子。我们表明，以这种方式定义的度量成为经典的大极限，在这个意义上，量子涨落的度量被抑制asdue的大因式分解属性。作为一个具体的例子，我们将我们的方法应用于二维非线性模型。我们计算的三维诱导度规，这是描述一个反德西特空间中的无质量限制。最后，我们讨论了未来研究的几个开放问题。
We propose a method to define a-dimensional geometry from a-dimensional quantum field theory in theexpansion. We first construct a-dimensional field theory from the-dimensional one via the gradient-flow equation, whose flow timerepresents the energy scale of the system such thatcorresponds to the ultraviolet andto the infrared. We then define the induced metric from-dimensional field operators. We show that the metric defined in this way becomes classical in the large-limit, in the sense that quantum fluctuations of the metric are suppressed asdue to the large-factorization property. As a concrete example, we apply our method to thenonlinearmodel in two dimensions. We calculate the 3D induced metric, which is shown to describe an anti-de Sitter space in the massless limit. Finally, we discuss several open issues for future studies.