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Entropy 2016, 18(6), 212;

Extended First Law for Entanglement Entropy in Lovelock Gravity

Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
Author to whom correspondence should be addressed.
Academic Editor: David Kubiznak
Received: 15 April 2016 / Revised: 23 May 2016 / Accepted: 24 May 2016 / Published: 30 May 2016
(This article belongs to the Special Issue Black Hole Thermodynamics II)
Full-Text   |   PDF [267 KB, uploaded 30 May 2016]


The first law for the holographic entanglement entropy of spheres in a boundary CFT (Conformal Field Theory) with a bulk Lovelock dual is extended to include variations of the bulk Lovelock coupling constants. Such variations in the bulk correspond to perturbations within a family of boundary CFTs. The new contribution to the first law is found to be the product of the variation δ a of the “A”-type trace anomaly coefficient for even dimensional CFTs, or more generally its extension δ a * to include odd dimensional boundaries, times the ratio S / a * . Since a * is a measure of the number of degrees of freedom N per unit volume of the boundary CFT, this new term has the form μ δ N , where the chemical potential μ is given by the entanglement entropy per degree of freedom. View Full-Text
Keywords: holography; entanglement entropy; Lovelock gravity holography; entanglement entropy; Lovelock gravity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Kastor, D.; Ray, S.; Traschen, J. Extended First Law for Entanglement Entropy in Lovelock Gravity. Entropy 2016, 18, 212.

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