## Abstract

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 φ4 theory in dimension d = 4 - ∈, extracting the CFT data to order ∈2.We also check our results by standard field theory methods, both in the large N and _ expansions. Finally, we briefly discuss the relation of our analysis to the problem of construction of local bulk operators in AdS/CFT.

Original language | English (US) |
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Article number | 024003 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 54 |

Issue number | 2 |

DOIs | |

State | Published - Dec 2020 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

## Keywords

- AdS/CFT correspondence
- conformal bootstrap
- conformal field theory