• Open Access

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

Kristan Jensen, Andy O’Bannon, Brandon Robinson, and Ronnie Rodgers
Phys. Rev. Lett. 122, 241602 – Published 19 June 2019
PDFHTMLExport Citation

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 D3 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.

  • Received 21 January 2019

DOI:https://doi.org/10.1103/PhysRevLett.122.241602

Published by the American Physical Society under the terms of the 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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

General PhysicsParticles & Fields

Authors & Affiliations

Kristan Jensen1,*, Andy O’Bannon2,†, Brandon Robinson2,‡, and Ronnie Rodgers2,§

  • 1Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
  • 2STAG Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom

  • *kristanj@sfsu.edu
  • a.obannon@soton.ac.uk
  • B.J.Robinson@soton.ac.uk
  • §R.J.Rodgers@soton.ac.uk

Article Text

Click to Expand

Supplemental Material

Click to Expand

References

Click to Expand
Issue

Vol. 122, Iss. 24 — 21 June 2019

Reuse & Permissions
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

×

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×