On correlation functions of BPS operators in $3d$ $\mathcal{N}=6$ superconformal theories

Abstract

We introduce a novel harmonic superspace for $3d$ $\mathcal{N}=6$ superconformal field theories that is tailor made for the study of correlation functions of BPS operators. We calculate a host of two- and three-point functions in full generality and put strong constraints on the form of four-point functions of some selected BPS multiplets. For the four-point function of $\frac{1}{2}$-BPS operators we obtain the associated Ward identities by imposing the absence of harmonic singularities. The latter imply the existence of a solvable subsector in which the correlator becomes topological. This mechanism can be explained by cohomological reduction with respect to a special nilpotent supercharge.

41 pages, v2: typos corrected, references added

References in corpus (18)

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• Fractional M2-branes
• Indices for Superconformal Field Theories in 3,5 and 6 Dimensions
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• Remarks on the Convergence Properties of the Conformal Block Expansion
• Superconformal partial waves in Grassmannian field theories
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• Giant Gravitons on AdS_4 x CP^3 and their Holographic Three-point Functions
• On the ABJM four-point amplitude at three loops and BDS exponentiation
• ABJ(M) Chiral Primary Three-Point Function at Two-loops
• The Morphology of N=6 Chern-Simons Theory
• An Extremal Chiral Primary Three-Point Function at Two-loops in ABJ(M)

Cited by in corpus (18)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Bootstrapping the half-BPS line defect
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• Long Multiplet Bootstrap
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Superconformal Blocks for SCFTs with Eight Supercharges
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• The topological line of ABJ(M) theory
• Bootstrapping (D, D) Conformal Matter
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Three-Point Functions in ABJM and Bethe Ansatz
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM