Aspects of CFTs on real projective space
Aspects of CFTs on real projective space
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DOI：
10.1088/1751-8121/abcf59
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发表时间：
2020-09
期刊：
影响因子：
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通讯作者：
S. Giombi;H. Khanchandani;Xinan Zhou
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文献类型：
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作者：
S. Giombi;H. Khanchandani;Xinan Zhou
本文对实射影空间RPd上的共形场理论进行了解析研究，重点讨论了标量算子的两点函数。由于保形对称性的部分破缺，它们是保形交叉比的非平凡函数，并被约束服从交叉方程。在回顾了RPd上相关器结构的基本事实之后，我们研究了一种简单的全息装置，该装置捕捉了RPd上边界相关器的基本特征。该分析基于商空间AdSd+1/Z2上的Witten图的计算，并得出两点函数的解析方法。特别地，我们认为交换Witten图的共形块分解的结构暗示了解析泛函的自然基础，它对共形块的作用使交叉方程变成一定的和规则。我们在维数d = 4−λ的φ 4理论的典型例子中测试了这种方法，提取了阶为λ 2的CFT数据。我们还通过标准场论方法检查了我们的结果，包括大N和λ展开。最后，简要讨论了本文的分析与AdS/CFT地区散货船建设问题的关系。
We present an analytic study of conformal field theories on the real projective space RPd , focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions of a conformal cross ratio and are constrained to obey a crossing equation. After reviewing basic facts about the structure of correlators on RPd , we study a simple holographic setup which captures the essential features of boundary correlators on RPd . The analysis is based on calculations of Witten diagrams on the quotient space AdSd+1/Z2 , and leads to an analytic approach to two-point functions. In particular, we argue that the structure of the conformal block decomposition of the exchange Witten diagrams suggests a natural basis of analytic functionals, whose action on the conformal blocks turns the crossing equation into certain sum rules. We test this approach in the canonical example of ϕ 4 theory in dimension d = 4 − ϵ, extracting the CFT data to order ϵ 2. We also check our results by standard field theory methods, both in the large N and ϵ expansions. Finally, we briefly discuss the relation of our analysis to the problem of construction of local bulk operators in AdS/CFT.