Embedding formalism for CFTs in general states on curved backgrounds
Embedding formalism for CFTs in general states on curved backgrounds
We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in d + 2 dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a d-dimensional conformal manifold, which is the physical spacetime where the CFTd lives. We propose a construction of CFTd n-point functions in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. This captures the contributions of non-vanishing 1-point functions of multi-stress-energy tensors, at least in holographic CFTs. We apply the formalism to 2-point functions of thermal CFT, finding exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs), and to CFTs on squashed spheres where no prior results are known and existing methods are difficult to apply, demonstrating the utility of the method.
Parisini, Enrico
b1e0f8e0-9464-4ff5-bbc5-d37eeebf4a2d
Skenderis, Kostas
09f32871-ffb1-4f4a-83bc-df05f4d17a09
Withers, Benjamin
e510375b-c5d2-4d5f-bd68-40ace13f0ec9
24 March 2023
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
(2023)
Embedding formalism for CFTs in general states on curved backgrounds.
Physical Review D, 107 (6), [066022].
(doi:10.1103/PhysRevD.107.066022).
Abstract
We present a generalisation of the embedding space formalism to conformal field theories (CFTs) on non-trivial states and curved backgrounds, based on the ambient metric of Fefferman and Graham. The ambient metric is a Lorentzian Ricci-flat metric in d + 2 dimensions and replaces the Minkowski metric of the embedding space. It is canonically associated with a d-dimensional conformal manifold, which is the physical spacetime where the CFTd lives. We propose a construction of CFTd n-point functions in non-trivial states and on curved backgrounds using appropriate geometric invariants of the ambient space as building blocks. This captures the contributions of non-vanishing 1-point functions of multi-stress-energy tensors, at least in holographic CFTs. We apply the formalism to 2-point functions of thermal CFT, finding exact agreement with a holographic computation and expectations based on thermal operator product expansions (OPEs), and to CFTs on squashed spheres where no prior results are known and existing methods are difficult to apply, demonstrating the utility of the method.
Text
PhysRevD.107.066022
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Accepted/In Press date: 10 March 2023
Published date: 24 March 2023
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Funding Information:
We thank Slava Rychkov for comments. The work of E. P. is supported by Royal Society Research Grants No. RGF/EA/181054 and No. RF/ERE/210267. K. S. and B. W. are supported in part by the Science and Technology Facilities Council (Consolidated Grant “Exploring the Limits of the Standard Model and Beyond”). B. W. is supported by a Royal Society University Research Fellowship.
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© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
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Local EPrints ID: 476595
URI: http://eprints.soton.ac.uk/id/eprint/476595
ISSN: 2470-0010
PURE UUID: 5e436357-00d4-419d-be09-6219cca0a5c4
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Date deposited: 09 May 2023 17:02
Last modified: 17 Mar 2024 03:57
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Enrico Parisini
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