Universal Entanglement and Boundary Geometry in Conformal Field Theory

Abstract

Employing a conformal map to hyperbolic space cross a circle, we compute the universal contribution to the vacuum entanglement entropy (EE) across a sphere in even-dimensional conformal field theory. Previous attempts to derive the EE in this way were hindered by a lack of knowledge of the appropriate boundary terms in the trace anomaly. In this paper we show that the universal part of the EE can be treated as a purely boundary effect. As a byproduct of our computation, we derive an explicit form for the A-type anomaly contribution to the Wess-Zumino term for the trace anomaly, now including boundary terms. In d=4 and 6, these boundary terms generalize earlier bulk actions derived in the literature.

35 pages text plus 17 pages appendices and references, 3 figures; v2 package conflict resolved; v3 refs added, claim regarding newness of boundary central charge in d=4 removed, factor of 3 typo fixed

References in corpus (10)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Entanglement entropy, conformal invariance and extrinsic geometry
• Entanglement Entropy, Trace Anomalies and Holography
• Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching
• Counterterms in Dimensionally Continued AdS Gravity
• Conformal anomalies of CFT's with boundaries
• c-theorem of the entanglement entropy
• Boundary F-maximization

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