Emergent spacetime

A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg in ful lment of the requirements for the degree of Master of Science. June 29, 2017.In this dissertation we explore the connection between entanglement and geometry. Recent work in the AdS/CFT correspondence has uncovered fascinating connections between quantum information and geometry, suggesting that entanglement in the CFT results in the emergence of spacetime in the bulk . We work in the 1/2 BPS sector of the duality between N = 4 super Yang Mills on R x S3 and IIB string theory on AdS5 S5. We aim to test this connection by calculating the Renyi entropies in the presence of 1/2 BPS operators heavy enough to deform the background geometry. This allows us to calculate the entanglement of these operators via the replica trick. The Ryu-Takayanagi formula relates this calculation to a minimal surface in the dual supergravity geometry, thus allowing us to observe how the boundary entanglement affects the bulk spacetime. We build a formula to calculate correlation functions of 1/2 BPS operators on the Riemann sheet that arises from the replica trick. This is a recursive formula based on group theory techniques. We demonstrate how the formula works for light operators and discuss how it can be generalised to include heavy operators by considering symmetric groups of higher order.LG201