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.

arXiv comment38 pages, 2 figures, 3 tables

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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