Some aspects of entanglement entropy

Abstract

Entanglement entropy has emerged as an important quantity in quantum field theory. In this report, we present some aspects of entanglement entropy in the context of string theory. We assume the AdS/CFT Correspondence. String theory has provided a microscopic description of black hole entropy in the case of certain black holes. We examine the relation between the black entropy and entanglement entropy. This relation is described in detail for a special case and comments are made about approaches in finding such a relation in general case. In the second and the main part of this report, we present some first and original attempts at studying the modular invariance of Rényi and entanglement entropies. We clarify subtle issues in the application of Replica Trick to theories at finite temperature. We propose a modular invariant expression for entanglement entropy for free fermion conformal field theories in 2 dimensions, with a finite size entangling interval and finite temperature. We study single Dirac fermion, two correlated Dirac fermions and multiple correlated Dirac fermions in detail. Comments are also made about the T-duality invariance and modular invariance of the Rényi entropy for a single free boson CFT. Our proposal is shown to obey several tests and is consistent with known answers in limiting situations