Shape Dependence of Holographic Rényi Entropy in Conformal Field Theories
Abstract
We develop a framework for studying the well-known universal term in the Rényi entropy for an arbitrary entangling region in four-dimensional conformal field theories that are holographically dual to gravitational theories. The shape dependence of the Rényi entropy Sn is described by two coefficients: fb(n ) for traceless extrinsic curvature deformations and fc(n ) for Weyl tensor deformations. We provide the first calculation of the coefficient fb(n ) in interacting theories by relating it to the stress tensor one-point function in a deformed hyperboloid background. The latter is then determined by a straightforward holographic calculation. Our results show that a previous conjecture fb(n )=fc(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
- E-Print:
- 7 pages, 1 figure