Spinning conformal blocks and applications

Conformal invariance is a concept that is common to many areas of theoretical physics; from critical phenomena in statistical and condensed matter system, through the description of particle physics at long distances, to quantum gravity via the holographic principle. The main focus of this work is the study of Conformal Field Theories (CFTs), which are conformally invariant quantum field theories. The extra symmetries in a CFT fix all the observables of the theory up to a set of numerical coefficients called “CFT data”, and furthermore they impose consistency conditions that completely characterize the space of valid CFTs. The quest for solving these consistency constraints is called the “conformal bootstrap program”, which has increased in popularity in the recent years due to its success. Nonetheless, the bootstrap program is far from complete. In particular, the conformal partial waves describing spinning fields are not fully understood yet.
In this thesis we present two developments in the computation of spinning partial waves in closed form for arbitrary space-time dimensions. Also we compute universal constraints on the CFT data related to the conformal stress-tensor in arbitrary dimensions, by combining two analytical bootstrap tools. Finally, we apply CFT techniques to gravity by providing a dictionary between spinning partial waves and geodesic objects living in the dual AdS theory.