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

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.

arXiv comment36 pages plus appendices, 5 figures, 5 tables

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Cited by in corpus (6)

• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• 1/3 BPS loops and defect CFTs in ABJM theory
• Analytic bootstrap for magnetic impurities
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Boundary bound states and integrable Wilson loops in ABJM