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Journal of High Energy Physics

, 2016:36

First Online: 12 December 2016Received: 11 August 2016Revised: 30 November 2016Accepted: 01 December 2016 Abstract

We consider higher derivative gravity and obtain universal relations for the shape coefficients fa, fb, fc of the shape dependent universal part of the Rényi entropy for four dimensional CFTs in terms of the parameters c, t2, t4 of two-point and three-point functions of stress tensors. As a consistency check, these shape coefficients fa and fc satisfy the differential relation as derived previously for the Rényi entropy. Interestingly, these holographic relations also apply to weakly coupled conformal field theories such as theories of free fermions and vectors but are violated by theories of free scalars. The mismatch of fa for scalars has been observed in the literature and is due to certain delicate boundary contributions to the modular Hamiltonian. Interestingly, we find a combination of our holographic relations which are satisfied by all free CFTs including scalars. We conjecture that this combined relation is universal for general CFTs in four dimensional spacetime. Finally, we find there are similar universal laws for holographic Rényi entropy in general dimensions.

KeywordsAdS-CFT Correspondence Classical Theories of Gravity Conformal Field Theory ArXiv ePrint: 1608.00328

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Autor: Chong-Sun Chu - Rong-Xin Miao

Fuente: https://link.springer.com/







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