From the Weyl anomaly to entropy of two-dimensional boundaries and defects
From the Weyl anomaly to entropy of two-dimensional boundaries and defects
We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of D≥3 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, b, obeys a c-theorem, as in 2D CFT. For a 2D defect, we show that another, d2, interpreted as the defect's 'conformal dimension,' must be non-negative by the Averaged Null Energy Condition (ANEC). We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by b and d2. Using this and known holographic results, we compute b and d2 for 1/2-BPS surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with b's c-theorem. Via free field and holographic examples we show that no universal 'Cardy formula' relates the central charges to thermal entropy.
Jensen, Kristan
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O'Bannon, Andrew
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Robinson, Brandon
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Rodgers, Ronald, James
50624100-db56-478e-9b46-0db869df1020
2019
Jensen, Kristan
1aa6bec5-5b04-4014-b008-ace89ed2884c
O'Bannon, Andrew
f0c14b6c-5b74-4319-8432-f9eba1e20cf3
Robinson, Brandon
56901315-b500-40af-9f3b-1b8cbbdfaffb
Rodgers, Ronald, James
50624100-db56-478e-9b46-0db869df1020
Jensen, Kristan, O'Bannon, Andrew, Robinson, Brandon and Rodgers, Ronald, James
(2019)
From the Weyl anomaly to entropy of two-dimensional boundaries and defects.
Physical Review Letters, 122, [241602].
(doi:10.1103/PhysRevLett.122.241602).
Abstract
We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of D≥3 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, b, obeys a c-theorem, as in 2D CFT. For a 2D defect, we show that another, d2, interpreted as the defect's 'conformal dimension,' must be non-negative by the Averaged Null Energy Condition (ANEC). We show that the EE of a sphere centered on a planar defect has a logarithmic contribution from the defect fixed by b and d2. Using this and known holographic results, we compute b and d2 for 1/2-BPS surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with b's c-theorem. Via free field and holographic examples we show that no universal 'Cardy formula' relates the central charges to thermal entropy.
Text
1812.08745
- Accepted Manuscript
More information
Accepted/In Press date: 10 May 2019
e-pub ahead of print date: 19 June 2019
Published date: 2019
Identifiers
Local EPrints ID: 430893
URI: http://eprints.soton.ac.uk/id/eprint/430893
ISSN: 1079-7114
PURE UUID: 90168d5b-0db8-42e9-b017-1de73fa02406
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Date deposited: 17 May 2019 16:30
Last modified: 16 Mar 2024 07:51
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Author:
Kristan Jensen
Author:
Brandon Robinson
Author:
Ronald, James Rodgers
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