Conformal defects and RG flows in ABJM

TL;DR

This paper explores defect conformal field theories in ABJM, analyzing RG flows triggered by marginal operators, and computes anomalous dimensions, g-theorems, and anomalies in the context of Wilson loops.

Contribution

It provides new insights into RG flows between defect CFTs in ABJM theory, including calculations of anomalous dimensions and the role of anomalies and framing.

Findings

Identified RG flows connecting BPS and non-BPS Wilson loop defect CFTs.

Computed anomalous dimensions of deforming operators.

Established g-theorems along the RG flows.

Abstract

Defects play a central role in many contexts, from condensed matter to quantum gravity. The situations in which the bulk theory is conformal and the defect inherits part of this symmetry -- the so-called defect conformal field theories (dCFTs) -- have recently received a lot of attention, also thanks to new powerful methods to tackle them, like supersymmetric localization, integrability or the bootstrap. A dCFT may be deformed by turning on marginally relevant operators, which trigger RG flows connecting different fixed points. A natural arena where this phenomenon can be explored are 3-dimensional Chern-Simons theories coupled to matter. These are in fact known to display a plethora of Wilson loops that can be used to define 1-dimensional dCFTs living on their contours. Here we discuss a few examples from an intricate web of RG flows connecting the dCFTs defined on the BPS and non-BPS Wilson loops of ABJM theory. We compute the anomalous dimensions of the deforming operators, establish g-theorems along the flows, and also discuss the role played by cohomological anomalies and framing.