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 CFTs. The Weyl anomaly of a 2D boundary or defect defines two or three central charges, respectively. One of these, , obeys a theorem, as in 2D CFT. For a 2D defect, we show that another, , 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 and . Using this and known holographic results, we compute and for -Bogomol’nyi-Prasad-Sommerfield surface operators in the maximally supersymmetric (SUSY) 4D and 6D CFTs. The results are consistent with ’s 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