Superconformal Line Defects in 3D

Abstract

We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.

Spin Impurities, Wilson Lines and Semiclassics

“…(2.5). 17 For instance, it is easy to verify that the sum over diagrams of order γ 2 0 s 2 , which are simply obtained by neglecting the path-ordering (i.e. dropping all the commutators) exponentiates the first γ 2 0 s 2 contribution in fig 6a.…”

“…For concreteness, we focus on rank-1 theories. 8 1/2-BPS Wilson loops in N ≥ 2 superconformal field theories (SCFTs) are among the most studied examples of DCFTs in the literature [68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85] (for a general approach to supersymmetric line defects in diverse dimensions see [16,17,86]). Notice that, in general, the large representation limit is of interest also for the study of non-Lagrangian theories, in which case superconformal defects are roughly labeled by the electric and magnetic charges of their IR representative in the Coulomb branch of the theory [75,77,81].…”

“…A more careful analysis indeed shows that a remarkable exponentiation takes place. 17 As a result, the logarithm of the g-function admits the following expansion in 15 The breakdown of perturbation theory for multilegged amplitudes, and its relation to semiclassics, was first analyzed in the context of multi-particle production -see e.g. [105,106].…”

“…In a different context, several works focused on the study of conformal gauge theories in the presence of line operators, especially in supersymmetric theories (see e.g. [15][16][17] and references therein). Building on similarities with the description of large spin impurities, in this work we will address the large representation limit of supersymmetric Wilson lines in N = 2 superconformal gauge theories, that is 1/2-BPS Wilson loops in which the size s of the labeling representation becomes large.…”

Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence

“…The technique used to establish the result, a cohomological equivalence between a deformation of the theory which is integrated over the entire spacetime and one which is restricted to a submanifold, is itself interesting. We believe it may have many additional applications, for instance to theories with defects (for a recent review, see [24]).…”