Multipoint Lightcone Bootstrap from Conformal Block Integrability

Abstract

Conformal field theories are universal descriptions of scale-invariant systems, ranging from critical phenomena all the way to theories of quantum gravity. In this context, the lightcone bootstrap program is an analytic approach to extracting physical data from the crossing symmetry equation of correlation functions. The equation is solved near lightcone singularities, where insertion points tend to lightlike separation. In this thesis, we make progress in extending the lightcone bootstrap to correlation functions of more than four fields. Our approach relies primarily on the integrability based theory of multipoint conformal blocks, which occupies the largest part of this work. The blocks, that is to say the kinematical constituents of a correlation function, are recast as wavefunctions of a many-body quantum integrable system. After constructing these integrable systems in full generality, we determine the corresponding system of differential equations that they entail for so called comb channel blocks. Following a detailed analysis of these differential equations, we then derive precise relations between higher and lower point blocks, as well as explicit solutions in various limits. Based on these results, we solve the five-point crossing equation at the first leading orders and lay the groundwork for the six-point comb channel lightcone bootstrap.