Flow equation, conformal symmetry, and anti-de Sitter geometry
Flow equation, conformal symmetry, and anti-de Sitter geometry
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流动方程、共角对称和反德西特几何
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Shuichiro Yokoyama
中科院分区：
文献类型：
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作者：
S. Aoki;Shuichiro Yokoyama
我们认为，反德西特（AdS）几何在d+1维自然出现从任意共形场理论在d维自由流方程。我们首先表明，从流场定义的诱导度规一般对应于量子信息度规，称为布勒斯或Helstrom度规，如果流场是适当的归一化。接下来，我们验证，诱导度量计算明确的自由流方程总是成为AdS度量时，理论是共形的。最后证明了d维量子平均后d维的共形对称性转化为d+1维的AdS等距性。这保证了AdS几何的出现，而无需显式计算。
We argue that the Anti-de-Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.