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.
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
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.
@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}
}
https://doi.org/10.1103/PhysRevLett.122.241602
Web of Science
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