Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory

TL;DR

This paper studies a special supermatrix operator in ABJ(M) theory's defect SCFT, revealing its properties at weak and strong coupling, and its unexpected appearance in Wilson loop equivalences.

Contribution

It introduces a covariant supermatrix framework for supercharges, proves the existence of a constant supermatrix operator multiplet, and explores its duality and role in Wilson loop relations.

Findings

The operator acquires a non-trivial anomalous dimension at weak coupling.

At strong coupling, it is conjectured to correspond to a string fluctuation bound state.

The operator appears in the cohomological equivalence between bosonic and fermionic Wilson loops.

Abstract

We investigate the one-dimensional defect SCFT defined on the $1/2$ BPS Wilson line/loop in ABJ(M) theory. We show that the supermatrix structure of the defect imposes a covariant supermatrix representation of the supercharges. Exploiting this covariant formulation, we prove the existence of a long multiplet whose highest weight state is a constant supermatrix operator. At weak coupling, we study this operator in perturbation theory and confirm that it acquires a non-trivial anomalous dimension. At strong coupling, we conjecture that this operator is dual to the lowest bound state of fluctuations of the fundamental open string in AdS$_4\times \mathbb{CP}_3$ around the classical $1/2$ BPS solution. Quite unexpectedly, this operator also arises in the cohomological equivalence between bosonic and fermionic Wilson loops. We also discuss some regularization subtleties arising in perturbative calculations on the infinite Wilson line.