Aspects of Entanglement Entropy in 3d N=2 Field Theories

Abstract

Entanglement entropy is an extremely important quantity in quantum field theory which specifies the amount of entanglement of quantum mechanical degrees of freedom across a spacelike entangling surface. On the other hand, supersymmetric localization is a powerful technique which reduces path integrals in supersymmetric gauge theories to finite dimensional integrals. In this thesis, we explore the possibilities of computing entanglement entropy (EE) in 3d N = 2 quantum field theories using localization. Firstly, examples of theories where the conformal symmetry is broken are studied, and the corrections to the EE along the induced RG flows are determined. Then, the focus will be mainly on understanding contributions to the EE due to deformations of the entangling region and to changes of its topology. This leads to evidence that the round disk maximizes the EE among entangling regions with non-simply connected topologies. More importantly, it is found that EE is independent of smooth deformations of the boundary of the entangling region due to powerful restrictions imposed by supersymmetry. Motivated by this and other considerations, we are led to a novel computation of EE of 3d N = 2 superconformal gauge theories at arbitrary YangMills coupling which reveals a particular UV divergence in its structure. Its presence results from sectors in the algebra of local operators of the theory which are charged under a gauge or global symmetry.