Strong coupling dynamics of defect RG flows in ABJM

TL;DR

This paper explores strong-coupling defect RG flows in ABJM theory using holography, analyzing string fluctuations in AdS$_4 imes ext{CP}^3$ to understand operator dimensions and boundary conditions.

Contribution

It provides a systematic holographic analysis of defect RG flows in ABJM at strong coupling, including subleading corrections and geometric interpretations.

Findings

1/2 BPS Wilson loop is IR stable.

1/6 BPS Wilson loop acts as a saddle point.

Non-supersymmetric Wilson loop emerges as UV fixed point.

Abstract

Wilson loop operators in ABJM theory provide a rich arena for studying defect conformal field theories (dCFTs) and the renormalization group (RG) flows connecting them. While these are well understood at weak coupling, a complete strong-coupling picture remains an open problem. In this paper, we present a systematic analysis of defect RG flows in ABJM at strong coupling, via holography. By examining fluctuations of fundamental strings in the AdS$_4 \times \mathbb{CP}^3$ background around classical AdS$_2$ solutions, we map worldsheet excitations to the operators in the dual dCFT which are responsible for the flows and determine their scaling dimensions, including subleading corrections from one-loop worldsheet effects. We show how different boundary conditions on string coordinates correspond to distinct operators and provide a geometric realization of the RG flows through interpolating boundary conditions. We apply this framework to fermionic 1/2 BPS, bosonic 1/6 BPS, and non-supersymmetric Wilson loops, establishing a coherent strong-coupling picture in which the 1/2 BPS loop is IR stable, the 1/6 BPS loop acts as a saddle point, and the non-supersymmetric configuration emerges as a natural UV fixed point. We also advance a proposal for the holographic dual of a second non-supersymmetric loop, in terms of averaging over Dirichlet boundary conditions.