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Title: From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects

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 if the averaged null energy condition holds in the presence of the defect. 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-Bogomol’nyi-Prasad-Sommerfield 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.

Authors:
; ; ;
Publication Date:
Research Org.:
San Francisco State Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1527054
Alternate Identifier(s):
OSTI ID: 1612020
Grant/Contract Number:  
SC0013682
Resource Type:
Published Article
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Name: Physical Review Letters Journal Volume: 122 Journal Issue: 24; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics; Anomalies; Conformal field theory; Weyl fermions

Citation Formats

Jensen, Kristan, O’Bannon, Andy, Robinson, Brandon, and Rodgers, Ronnie. From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects. United States: N. p., 2019. Web. doi:10.1103/PhysRevLett.122.241602.
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Jensen, Kristan, O’Bannon, Andy, Robinson, Brandon, & Rodgers, Ronnie. From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects. United States. https://doi.org/10.1103/PhysRevLett.122.241602
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Jensen, Kristan, O’Bannon, Andy, Robinson, Brandon, and Rodgers, Ronnie. Wed . "From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects". United States. https://doi.org/10.1103/PhysRevLett.122.241602.
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@article{osti_1527054,
title = {From the Weyl Anomaly to Entropy of Two-Dimensional Boundaries and Defects},
author = {Jensen, Kristan and O’Bannon, Andy and Robinson, Brandon and Rodgers, Ronnie},
abstractNote = {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 if the averaged null energy condition holds in the presence of the defect. 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-Bogomol’nyi-Prasad-Sommerfield 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.},
doi = {10.1103/PhysRevLett.122.241602},
journal = {Physical Review Letters},
number = 24,
volume = 122,
place = {United States},
year = {2019},
month = {6}
}
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https://doi.org/10.1103/PhysRevLett.122.241602
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