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Bekenstein-Hawking entropy as topological entanglement entropy

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Abstract

Black holes in 2+1 dimensions enjoy long range topological interactions similar to those of non-abelian anyon excitations in a topologically ordered medium. Using this observation, we compute the topological entanglement entropy of BTZ black holes via the established formula S top = log(\( S_0^a \)), with \( S_b^a \) the modular S-matrix of the Virasoro characters χ a (τ). We find a precise match with the Bekenstein-Hawking entropy. This result adds a new twist to the relationship between quantum entanglement and the interior geometry of black holes. We generalize our result to higher spin black holes, and again find a detailed match. We comment on a possible alternative interpretation of our result in terms of boundary entropy.

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Authors and Affiliations

  1. Department of Physics, Princeton University, Washington Road, Princeton, NJ, 08544, U.S.A.

    Lauren McGough & Herman Verlinde

  2. Princeton Center for Theoretical Sciences, Princeton University, Washington Road, Princeton, NJ, 08544, U.S.A.

    Herman Verlinde

Authors
  1. Lauren McGough
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  2. Herman Verlinde
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Correspondence to Lauren McGough.

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ArXiv ePrint: 1308.2342

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McGough, L., Verlinde, H. Bekenstein-Hawking entropy as topological entanglement entropy. J. High Energ. Phys. 2013, 208 (2013). https://doi.org/10.1007/JHEP11(2013)208

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