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, d_{2}, 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 d_{2}. Using this and known holographic results, we compute b and d_{2} 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.
Highlights
Introduction.—conformal field theory (CFT) play a central role in many branches of physics
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
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
Summary
Extending a key result of Ref. [23]. Using this and known holographic results, we compute these central charges for certain 1=2-Bogomol’nyi-Prasad-Sommerfield (BPS) surface operators in the maximally SUSY 4D and 6D CFTs. Using this and known holographic results, we compute these central charges for certain 1=2-Bogomol’nyi-Prasad-Sommerfield (BPS) surface operators in the maximally SUSY 4D and 6D CFTs. for the free massless scalar and fermion 3D BCFTs and for 2D defects holographically dual to probe branes, we calculate s ∝ T at the boundary or defect, with no universal relation between the proportionality coefficient and central charges. Conventions.—We start with a local, unitary, Lorentzian CFT on a D ≥ 3 spacetime M with coordinates xμ (μ 1⁄4 0; 1; ...; D − 1) and metric gμν, which we will call the “bulk” CFT. We parametrize Σ ↪ M by embedding functions XμðyÞ such that Σ’s induced metric is γab ≡ ∂aXμ∂bXνgμν. We denote M’s covariant derivative as ∇μ and Σ’s induced covariant derivative as
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