Perturbative entanglement thermodynamics for AdS spacetime: Renormalization
arXiv:1507.03836
Abstract
We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that `boosted' AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately `renormalized' at the second order due to the corrections. We work in the perturbative regime where .
arXiv comment14 pages, 1 figure; V2: Details and explanations added, typo corrections; V3: Bad typo in eq.28 corrected, no change of results