Connor Behan, "New approaches to conformal manifolds in one and two dimensions"

Monday 19 Nov 2018, 14:00 → 16:00 Europe/Zurich

4/3-006 - TH Conference Room (CERN)

The bootstrap program for quantum field theories can be broadly divided into two complementary efforts. One is concerned with classifying isolated conformal field theories and the other seeks to understand deformations away from these CFTs along a renormalization group flow. I will discuss the borderline case in which a manifold of CFTs can be traversed by an exactly marginal deformation. While these conformal manifolds were first studied in the context of string worldsheets, they have also become important in more bottom-up physical systems. Throughout this talk, I will focus on a set of nonlinear differential equations that apply whenever there is a discrete non-degenerate spectrum of operators with data depending on an exactly marginal coupling. These equations present a scenario in which conformal perturbation theory can be used to infer non-perturbative results. They also offer a tantalizing hope of computing the spectrum of a non-trivial conformal manifold to arbitrary precision. I will carry out a survey of some of the known conformal manifolds with the goal of identifying particular theories that are most amenable to this approach.