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
