Conformal bootstrap and thermalization in holographic CFTs

Abstract

This thesis covers a number of topics in conformal field theories that are supposed to have gravity duals according to the AdS/CFT correspondence. We use the conformal bootstrap in the Regge and lightcone limits as the technique for studying these theories. We compute the operator product expansion coefficients of the multi-stress tensor operators with spin greater than zero with two identical scalar primary operators. We also explore the thermal properties of the stress tensor sector by studying the large central charge conformal field theories at finite temperature. We show that all multi-stress operators have the thermal expectation value equal to the three-point function with two identical scalar primary operators with the conformal dimension of the order of central charge. Therefore, we say that the stress tensor sector satisfies the diagonal part of the Eigenstate Thermalization Hypothesis and that it thermalizes in large central charge theories.