Title: Bootstrapping from a boundary point of view
Description: In this work, we study two problems in quantum field theory from a boundary point of view. Our perspective is motivated by the bootstrap philosophy, which aims to understand how principles such as kinematics, unitarity, and symmetry constrain physical observables. Regarding kinematics, we actually first relax the unitarity constraint and investigate thenon-unitary representations of the boundary superconformal algebra for AdS4 with N = 2 supercharges. In particular, we identify multiplets containing partially massless (PM) fields, as well as other exotic shortening conditions and structures exclusive to the nonunitary regime. Then, turning on interactions, we study a problem centered in dynamics: we investigate the structure of the flat space wavefunctional in scalar field theories with nonlinearly realized symmetries. In particular, we highlight the so-called exceptional scalar field theories, which are the nonlinear sigma model, Dirac-Born-Infeld, and (special) galileon theories. We find that nonlinearly realized symmetries imply soft theorems which must be obeyed by the wavefunction.

Moreover, we develop bootstrap techniques utilizing this information along with the singularity structure of the wavefunction to fix its form. In addition, we systematize this construction into a novel set of recursion relations.