The Noether charge entropy in anti-deSitter space and its field theory dual

Abstract

We express the Noether charge entropy density of a black brane in anti-deSitter space in terms of local operators in the anti-deSitter space bulk. We find that Wald's expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. We do so by calculating the value of the entropy density at the anti-deSitter space boundary and applying the standard rules of the AdS/CFT correspondence. We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultra-violet to the infra-red. We discuss the cases of Einstein-Hilbert theory and f(R) theories in detail and make general comments about more complicated cases.

21 pages; v2: minor corrections, results unchanged; v3: typos corrected

References in corpus (5)

• f(R) Theories Of Gravity
• Boundary Terms, Variational Principles and Higher Derivative Modified Gravity
• Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling
• AdS/CFT correspondence and Geometry
• Sound Mode Hydrodynamics from Bulk Scalar Fields

Cited by in corpus (6)

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• Wave function of the quantum black hole
• Graviton n-point functions for UV-complete theories in Anti-de Sitter space
• Non-perturbative unitarity constraints on the ratio of shear viscosity to entropy density in UV complete theories with a gravity dual
• Geometrothermodynamics for Black holes and de Sitter Space
• Gravitational entropy and thermodynamics away from the horizon