Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects

By K. Jensen, A. O’Bannon. 2013

144 citations recorded by the source corpus.

We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For boundary CFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein–Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi’s conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the Renyi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e58999c9086e2754fb343a6414157246bf95a480

How researchers see this paper

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In Astronomy and Astrophysics

1. R. Myers
2. H. Casini
3. M. Huerta
4. T. Takayanagi
5. A. Yale
6. T. Nishioka
7. T. Faulkner
8. M. Rangamani

In Nuclear and High Energy Physics

1. R. Myers
2. H. Casini
3. T. Takayanagi
4. M. Huerta
5. A. Yale
6. T. Nishioka
7. T. Faulkner
8. M. Rangamani

In Statistical and Nonlinear Physics

1. R. Myers
2. H. Casini
3. M. Huerta
4. A. Yale
5. T. Takayanagi
6. T. Nishioka
7. Aninda Sinha
8. T. Faulkner

Citations in the corpus

• Exact results for the entanglement entropy and the energy radiated by a quark (2013, unknown): “As noted in [8, 9, 10, 11],”
• Mutual information and the F-theorem (2015, background): “Recently, entanglement entropy was also discussed as a framework to extend the two-dimensional g-theorem [17, 18] to higher dimensional boundary c-theorems [19, 20] — see also [21].”