The ambient space formalism
The ambient space formalism
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.
AdS-CFT Correspondence, Differential and Algebraic Geometry, Scale and Conformal Symmetries, Thermal Field Theory
Parisini, Enrico
b1e0f8e0-9464-4ff5-bbc5-d37eeebf4a2d
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
27 May 2024
Parisini, Enrico
b1e0f8e0-9464-4ff5-bbc5-d37eeebf4a2d
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
Parisini, Enrico, Skenderis, Kostas and Withers, Benjamin
(2024)
The ambient space formalism.
Journal of High Energy Physics, 2024 (5), [296].
(doi:10.1007/JHEP05(2024)296).
Abstract
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.
Text
Ambient_Embedding
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Text
JHEP05(2024)296
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Accepted/In Press date: 30 April 2024
Published date: 27 May 2024
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© The Author(s) 2024.
Keywords:
AdS-CFT Correspondence, Differential and Algebraic Geometry, Scale and Conformal Symmetries, Thermal Field Theory
Identifiers
Local EPrints ID: 490739
URI: http://eprints.soton.ac.uk/id/eprint/490739
ISSN: 1126-6708
PURE UUID: 5bdcafb3-338a-48e0-91f3-fd8093d004de
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Date deposited: 04 Jun 2024 17:09
Last modified: 18 Jun 2024 01:44
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Author:
Enrico Parisini
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