Large N Phase Transitions, Finite Volume, and Entanglement Entropy

Holographic studies of the entanglement entropy of field theories dual to charged and neutral black holes in asymptotically global AdS4 spacetimes are presented. The goal is to elucidate various properties of the quantity that are peculiar to working in finite volume, and to gain access to the behaviour of the entanglement entropy in the rich thermodynamic phase structure that is present at finite volume and large N. The entropy is followed through various first order phase transitions, and also a novel second order phase transition. Properties of a specific heat in the neighbourhood of the critical point are computed. Behaviour is found that contrasts interestingly with an earlier holographic study of a second order phase transition dual to an holographic superconductor.