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.

36 pages plus appendices, 5 figures, 5 tables

References in corpus (14)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Generalized Global Symmetries
• Fractional M2-branes
• Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Integrability and Conformal Bootstrap: One Dimensional Defect CFT
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at strong coupling
• Towards the exact Bremsstrahlung function of ABJM theory
• Structure Constants of Defect Changing Operators on the 1/2 BPS Wilson Loop
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• New BPS Wilson loops in $\mathcal{N}\text{= 4}$ circular quiver Chern-Simons-matter theories
• Localization and Duality for ABJM Latitude Wilson Loops
• On the infrared behaviour of 3d Chern-Simons theories in N=2 superspace

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