Studies of superconformal field theories using GLSM and conformal bootstrap

Abstract

In this thesis, we study strongly interacting superconformal field theories in two and three dimensions. In two dimensions, we investigate N = (0, 2) gauge theories using the gauged linear sigma models (GLSM). In those theories, we identify simple mechanism by which worldsheet description of H-flux satisfying Green-Schwarz Bianchi identity arises. Under the renormalization group flow, we argue that these models flow into superconformal fixed points describing string theory compactifications backgrounds with non-trivial H-flux turned on. By analyzing quantum-consistency of effective theories with such mechanism, we identify conditions under which these theories to become interacting superconformal field theories in the infrared. In three dimensions, we study maximally supersymmetric (N = 8) conformal field theories by conformal bootstrap approach. We focus on studying the four-point function of stress-tensor multiplet. The superconformal blocks for the four-point function are computed by analyzing superconformal Ward identity. Using these blocks, we study crossing symmetry constraints both numerically and analytically. Doing so, we obtain universal bounds and exact relations of N = 8 superconformal field theory data.