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Weyl anomalies of four dimensional conformal boundaries and defects

Weyl anomalies of four dimensional conformal boundaries and defects
Weyl anomalies of four dimensional conformal boundaries and defects
Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT’s Weyl tensor. For a co-dimension one boundary or defect (i.e. d = 5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a “central charge” that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples: monodromy and conical defects of free, massless scalars and Dirac fermions in d = 6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi’s AdS/BCFT with d = 5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.
Anomalies in Field and String Theories, Boundary Quantum Field Theory, Conformal Field Theory, Field Theories in Higher Dimensions
1126-6708
Chalabi, Adam
fdf2f8ce-9b0e-44a1-b6e6-202e0ccccb7c
Herzog, Christopher P.
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Robinson, Brandon
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Sisti, Jacopo
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O'bannon, Andrew
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Chalabi, Adam
fdf2f8ce-9b0e-44a1-b6e6-202e0ccccb7c
Herzog, Christopher P.
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Robinson, Brandon
56901315-b500-40af-9f3b-1b8cbbdfaffb
Sisti, Jacopo
d0865320-17e5-48b6-a89e-6b46c8e88f10
O'bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3

Chalabi, Adam, Herzog, Christopher P., Robinson, Brandon, Sisti, Jacopo and O'bannon, Andrew (2022) Weyl anomalies of four dimensional conformal boundaries and defects. Journal of High Energy Physics, 2022 (2), [166]. (doi:10.1007/JHEP02(2022)166).

Record type: Article

Abstract

Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT’s Weyl tensor. For a co-dimension one boundary or defect (i.e. d = 5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a “central charge” that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples: monodromy and conical defects of free, massless scalars and Dirac fermions in d = 6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi’s AdS/BCFT with d = 5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.

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More information

e-pub ahead of print date: 21 February 2022
Published date: 21 February 2022
Additional Information: Publisher Copyright: © 2022, The Author(s).
Keywords: Anomalies in Field and String Theories, Boundary Quantum Field Theory, Conformal Field Theory, Field Theories in Higher Dimensions

Identifiers

Local EPrints ID: 457598
URI: http://eprints.soton.ac.uk/id/eprint/457598
ISSN: 1126-6708
PURE UUID: 0d94f5d7-4fc7-4b78-9ead-6c29aba77532
ORCID for Andrew O'bannon: ORCID iD orcid.org/0000-0001-7862-783X

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Date deposited: 13 Jun 2022 16:55
Last modified: 25 Jun 2022 01:48

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Contributors

Author: Adam Chalabi
Author: Christopher P. Herzog
Author: Brandon Robinson
Author: Jacopo Sisti
Author: Andrew O'bannon ORCID iD

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