Abstract
In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary $c$-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk. In this paper we verify this for higher derivative theories. We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function. We also prove that given a theory of gravity described by a local covariant action in the bulk a sufficient condition to ensure holographic c-theorem is that the second law of causal horizon thermodynamics be satisfied by the theory. This allows us to explicitly construct holographic c-function in a theory where there is curvature coupling between gravity and matter and standard null energy condition cannot be defined although second law is known to hold. Based on the duality between c-theorem and the second law of causal horizon thermodynamics proposed in arXiv:1508.01343 [hep-th] and the supporting calculations of this paper we conjecture that every Unitary higher derivative theory of gravity in AdS satisfies the second law of causal horizon thermodynamics. If this is not true then c-theorem will be violated in a unitary Lorentz invariant field theory.
Highlights
Two AdS critical points [10,11,12,13,14,15,16].1 The holographic version of the c-theorem is proved by showing the existence of a function which decreases monotonically from the UV-AdS to the IR-AdS as a result of the field equations and gives the central charges when evaluated at the end points of the flow
In arXiv:1508.01343 [hep-th], one of the authors proposed that in AdS/CFT the gravity dual of the boundary c-theorem is the second law of thermodynamics satisfied by causal horizons in AdS and this was verified for Einstein gravity in the bulk
We pick up theories for which an entropy expression satisfying the second law exists and show that the entropy density evaluated on the causal horizon in a RG flow geometry is a holographic c-function
Summary
We will briefly review the contents of [17] and discuss some notations. AdS region which develops near the Poincare horizon, z → ∞ This metric has no global scaling isometry because dilatation is broken along the RG-flow. In [17] it was proposed that the boundary RG-flow is dual to the (thermo) dynamics of causal horizons caused by the breaking of the scaling isometry in the bulk. The holographic c-function in this framework was given by the Bekenstein-Hawking entropy density of the dynamical causal horizon (2.9) This directly relates the second law for causal horizons in AdS5 to the unitarity of the boundary theory in the form of c-theorem. As z increases the null geodesic generators of the causal horizon interpolate between the UV-AdS and the IR-AdS
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
