Entanglement in Quantum Field Theory and Quantum Gravity

Abstract

A quantum mechanical theory of the world leads to some surprising new phenomena, which are impossible to explain using our knowledge of classical mechanics. One such phenomenon is entanglement, which has no classical mechanical counterpart. In recent years, this phenomenon has provided deep insights into Quantum Field Theory and even Quantum Gravity. For example, in AdS/CFT,thetheoryofentanglementcanbeusedtoderivetheEinsteinequationsinthebulk theory of gravity. Entanglement has also provided a deep connection between theories of gravity and quantum error correcting codes. Perhaps the most interesting aspect of this phenomenon is its connection to information loss in evaporating Black Holes. Therefore, developing a better understanding of entanglement is crucial in formulating a theory of Quantum Gravity. In this thesis, we explore one of the most beautiful aspects of entanglement in the context of AdS/CFT, the Ryu-Takayanagi formula, which gives an interpretation of entanglement entropy in a CFT in terms of geometric quantum in the holographic dual theory of gravity. Several consistency checks of this formula have been provided, by comparing the entanglement entropy in the boundary theory with the answer obtained by a bulk computation. Proposals to generalize the Ryu-Takayanagi formula to include quantum e↵ects in the bulk theory of gravity have also been reviewed.