The holographic dual of Rényi relative entropy
Abstract
The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT's [1]. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime [1]. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime [2]. In this paper, we introduce a one-parameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT's and find a one-parameter generalization of the aforementioned known results about the relative entropy. We also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- August 2019
- DOI:
- 10.1007/JHEP08(2019)099
- arXiv:
- arXiv:1904.08433
- Bibcode:
- 2019JHEP...08..099B
- Keywords:
-
- AdS-CFT Correspondence;
- Black Holes;
- Classical Theories of Gravity;
- Conformal Field Theory;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Quantum Physics
- E-Print:
- 37 pages, 3 figures. V3: added references