Particle Theory Seminar: Nima Lashkari, MIT, “Holographic relative entropy”

Relative entropy is a measure of distinguishability of states and plays a central in quantum information theory. We argue that it is a natural generalization of free energy to far from equilibrium states. A generalization of the standard replica trick computes the relative entropy of arbitrary states in quantum field theory. We consider holographic CFTs and show that relative entropy with respect to vacuum for ball shaped regions is dual to the change in the conserved charge associated with a certain diffeomorphism in the bulk. This new entry in holography can be used to constrain effective theories appearing in the low-energy of quantum gravity.