Momentum Space Bootstrap of Conformal Correlation Functions

Abstract

Correlation functions are one of the most important objects in CFTs. Momentum space CFT correlation functions have wide range of applicability in contexts of cosmology, con- densed matter etc. CFT correlators in momentum space also allow us to make a connection between conformal and S-matrix bootstrap. However, usual techniques of calculating the 3-point CFT correlators using conformal invariance is not very efficient for 4-point or higher point correlators having a spinning operator insertion. To gain insight we look for theories with more symmetry constraints. One such class of theories are theories with higher spin symmetry or with slightly broken higher spin symmetries. These are important classes of thoeries as they have a gravity dual, exhibit strong weak duality, non supersymmetric duality etc. In these theories calculating CFT correlation functions is quite difficult. However, we circumvent this problem by mapping the correlators in slightly broken higher spin theory correlators to free theory correlators. Thus, the higher spin approach allows us to analyse these correlators in a non-perturbative manner. Hence we map the slightly broken higher spin theories which are interacting CFTs to the free CFTs.