Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories
Abstract
We develop a framework for studying the wellknown universal term in the Rényi entropy for an arbitrary entangling region in fourdimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy S_{n} is described by two coefficients: f_{b}(n ) for traceless extrinsic curvature deformations and f_{c}(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient f_{b}(n ) in interacting theories by relating it to the stress tensor onepoint function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture f_{b}(n )=f_{c}(n ), motivated by surprising evidence from a variety of free field theories and studies of conical defects, fails holographically.
 Publication:

Physical Review Letters
 Pub Date:
 June 2016
 DOI:
 10.1103/PhysRevLett.116.251602
 arXiv:
 arXiv:1602.08493
 Bibcode:
 2016PhRvL.116y1602D
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 7 pages, 1 figure