Supersymmetric Dualities and Quantum Entanglement in Conformal Field Theory

Abstract

Conformal field theory (CFT) has been under intensive study for many years. The scale invariance, which arises at the fixed points of renormalization group in relativistic quantum field theory (QFT), is believed to be enhanced to the full conformal group. In this dissertation we use two tools to shed light on the behavior of certain conformal field theories, the supersymmetric localization and the quantum entanglement Renyi entropies.

The first half of the dissertation surveys the infrared (IR) structure of the N = 2 supersymmetric quantum chromodynamics (SQCD) in three dimensions. The recently developed F-maximization principle shows that there are richer structures along conformal fixed points compared to those in N = 1 SQCD in four dimensions. We refer to one of the new phenomena as a “crack in the conformal window”. Using the known IR dualities, we investigate it for all types of simple gauge groups. We see different decoupling behaviors of operators depending on the gauge group. We also observe that gauging some flavor symmetries modifies the behavior of the theory in the IR.

The second half of the dissertation uses the Renyi entropy to understand the CFT from another angle. At the conformal fixed points of even dimensional QFT, the entanglement entropy is known to have the log-divergent universal term depending on the geometric invariants on the entangling surface. We make an observation about the universal term in free four-dimensional CFT Renyi entropy. In particular, we study the subleading term of three-dimensional Renyi entropy with circular entangling surface for massive free scalar. Then, we study the importance of boundary terms in computing Renyi entropy. We also resolve the issue of Renyi entropy around q = 1 in N = 4 Super-Yang-Mills theory.