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Main Authors: Parisini, Enrico, Skenderis, Kostas, Withers, Benjamin
Format: Preprint
Published: 2023
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Online Access:https://arxiv.org/abs/2312.03820
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author Parisini, Enrico
Skenderis, Kostas
Withers, Benjamin
author_facet Parisini, Enrico
Skenderis, Kostas
Withers, Benjamin
contents We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) $n$-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography.
format Preprint
id arxiv_https___arxiv_org_abs_2312_03820
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The Ambient Space Formalism
Parisini, Enrico
Skenderis, Kostas
Withers, Benjamin
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Differential Geometry
We present a new formalism to solve the kinematical constraints due to Weyl invariance for CFTs in curved backgrounds and/or non-trivial states, and we apply it to thermal CFTs and to CFTs on squashed spheres. The ambient space formalism is based on constructing a class of geometric objects that are Weyl covariant and identifying them as natural building blocks of correlation functions. We construct (scalar) $n$-point functions and we illustrate the formalism with a detailed computation of 2-point functions. We compare our results for thermal 2-point functions with results that follow from thermal OPEs and holographic computations, finding exact agreement. In our holographic computation we also obtain the OPE coefficient of the leading double-twist contribution, and we discuss how the double-twist coefficients may be computed from the multi-energy-momentum contributions, given knowledge of the analytic structure of the correlator. The 2-point function for the CFT on squashed spheres is a new result. We also discuss the relation of our work to flat holography.
title The Ambient Space Formalism
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Differential Geometry
url https://arxiv.org/abs/2312.03820