Spinning Correlators at Finite Temperature

Sammanfattning

This master thesis is framed in the striking correspondence between gravity theories in Anti-de Sitter spacetime (AdS) and Conformal Field Theories (CFT). This is usually known as AdS/CFT duality and relates gravity theories in the bulk with CFTs that live in their conformal boundary. We start by presenting the notion of CFTs and some of the results and techniques that are widely used in this field. This includes conformal correlators for scalar and spin operators, the state-operator correspondence and the operator product expansion (OPE) of operators. The embedding formalism and the index-free notation to encode tensors in polynomials are also discussed and used throughout this work. The basic notions of AdS are outlined and CFT at finite temperature is then introduced. We include a review of thermal blocks and thermal coefficients for a thermal two-point function between scalar fields in mean field theory. We then analyse the thermal two-point function for conserved currents, which was not known in the literature. Finally, we start a study of its thermal blocks and thermal coefficients for the mean field theory application.