The topological line of ABJ(M) theory

Abstract

We construct the one-dimensional topological sector of $\mathcal{N}=6$ ABJ(M) theory and study its relation with the mass-deformed partition function on $S^3$. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at twoloop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge $c_T$ of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

38 pages, 2 figures, 3 tables

References in corpus (13)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Fractional M2-branes
• Notes on SUSY Gauge Theories on Three-Sphere
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Supersymmetric Wilson loops on S^3
• Bootstrap equations for $\mathcal{N}=4$ SYM with defects
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Giant Wilson Loops and AdS${}_2$/dCFT${}_1$
• Topological Correlators and Surface Defects from Equivariant Cohomology
• ABJ(M) Chiral Primary Three-Point Function at Two-loops

Cited by in corpus (7)

• One-Dimensional Sectors From the Squashed Three-Sphere
• Constant primary operators and where to find them: The strange case of BPS defects in ABJ(M) theory
• On the abundance of supersymmetric strings in $Ad{S}_3\times S^3\times S^3\times S^1$ describing BPS line operators
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Three-Point Functions in ABJM and Bethe Ansatz
• Framing fermionic Wilson loops in ABJ(M)
• Generating functions for Higgs/Coulomb branch operators from 1d-3d cohomological equivalence