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

Understand

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.