A coarse-grained generalized second law for holographic conformal field theories. (11th February 2016)

• Record Type: Journal Article
• Authors: Bunting, William; Fu, Zicao; Marolf, Donald
• Is Part Of: Classical and quantum gravity. Volume 33:Number 5(2016:Mar.)
• Publication Date: 2016-02-11
• Subjects: generalized second law -- holographic entropy -- holographic quantum field theory; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/5/055008
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: We consider the universal sector of a dimensional large- N strongly interacting holographic CFT on a black hole spacetime background B . When our CFT d is coupled to dynamical Einstein–Hilbert gravity with Newton constant G d, the combined system can be shown to satisfy a version of the thermodynamic generalized second law (GSL) at leading order in G d . The quantity is non-decreasing, where is the (time-dependent) area of the new event horizon in the coupled theory. Our S CFT is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information—a quantity in turn defined in the AdS dual by the renormalized area of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Another corollary, given by setting states that no finite process taken as a whole can increase the renormalized free energy with constants set by This latter corollary constitutes a 2nd law for appropriate non-compact AdS event horizons.