Novel approaches to strongly coupled field theories

Abstract

Recently, various ideas have resulted in enormous advances in the understanding of strongly coupled field theories and in particular of conformal field theories. From string theory, the AdS/CFT correspondence has allowed field theory computation previously impossible to perform including exact large-N results for 4 dimensional N=4 super Yang-Mills theory. From field theory, the conformal bootstrap has provided new numerical techniques to compute criticaI exponents and two and three point functions by relying solely on symmetries and consistency constraints of the theory. Even more recently, one of us, P. Vieira, together with collaborators, has started to explore the extension of conformal bootstrap ideas to the more general case of massive theories. The basic idea is to use ali symmetries, unitarity and analyticity constraints to put bounds on parameters that determine the S-matrix. For example the residue of a given pole that physically represents the strength of the interaction between a particle and its bound state. In certain cases, the bounds are saturated by well-known theories giving-them a new interpretation and calculational possibilities. In this project we plan to expand and generalize those results by looking for quantities that are bounded by the constraints imposed on the S-matrix. As a result we expect to systematize this novel approach to strongly coupled theories that allows to define a quantum field theory solely by physical constraints and maximization problems. (AU)