Linear defects and one-dimensional sectors in three dimensional supersymmetric gauge theories

Abstract

In this thesis, we study three-dimensional supersymmetric gauge theories with extended supersymmetry. Particular care is given to the ABJM model. It is a N = 6 supersymmetric Chern-Simons matter theory, depending on a parameter k. The model interpolates between weak coupling and strong coupling regimes. In the former case, the weak coupling limit of the QFT is reliable. In the latter case, the theory is well described by the gravitational dual, which is M-theory on AdS4 × S^7/Z_k. We focus on observables constrained by N ≥ 4 supersymmetry, amenable of exact results. We will consider two types of one-dimensional subsectors. The first is a set of local operators, whose correlation functions are captured by a one-dimensional topological the- ory. The second is a family of loop operators known as latitude, characterized by a real parameter. The first two chapters provide a review of the relevant models and of the methods to study them. Specifically, Chapter 1 contains an introduction to various aspects of super- symmetric gauge theories in three dimensions. In Chapter 2 we review the localization technique, and we apply it to 3d gauge theories. We use the result to explore some re- markable features of the ABJM model, like the infra-red dualities for Chern-Simon level equal to one with a UV N = 4 SYM avatar. In Chapter 3 we present our results for the topological sector. We relate integrated topological correlation functions to derivatives of the mass deformed partition function, confirming a pre-existing conjecture. We apply and test the formula at weak coupling in ABJM. Chapter 4 is devoted to an introduction to BPS Wilson and vortex loop operators in 3d. We also review the construction of bosonic and fermionic Wilson loops in ABJM. We frame the discussion in terms of conformal defects. In chapter 5 we derive a matrix model for the latitude Wilson loop in ABJM, proving an existing conjecture. We also extend the result to all N ≥ 4 gauge theories. In Chapter 6 we relate the latitude Wilson loop in ABJM to a novel bound state of Wilson-vortex loop in the dual theory. We realize this dual operator as a one-dimensional quantum mechanics coupled to the bulk.