Superconformal invariants and spinning correlators in 3d $\mathcal{N}=2$ SCFTs

Abstract

We construct superconformal invariants in superspace which are used to build 3-point correlators of spinning operators in general $\mathcal{N}=2$ superconformal field theories in three dimensions. Our systematic analysis includes various relations between these invariants and provides a minimal set of parity-even and parity-odd invariants which is further used to construct general 3-point functions in any 3d $\mathcal{N}=2$ SCFT. For conserved (super)currents, we explicitly compute various 3-point functions using Wick contractions in the free field case, and express them in terms of the constructed parity-even invariants. We give evidence through examples for the claim that the 3-point function of conserved currents generally comprises of two parts - a parity-even piece coming from the free theory, and a parity-odd piece.

arXiv commentv3, 27 pages; a few typos corrected and a footnote added; final version published in EPJC (Particles and Fields)

References in corpus (24)

• Implications of Conformal Invariance in Field Theories for General Dimensions
• Spinning Conformal Correlators
• On graviton non-Gaussianities during inflation
• Implications of conformal invariance in momentum space
• Constraining conformal field theories with a slightly broken higher spin symmetry
• Superconformal Symmetry, Correlation Functions and the Operator Product Expansion
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman's Master Integrals
• Bootstrapping the Three-Dimensional Supersymmetric Ising Model
• Bootstrapping SCFTs with Four Supercharges
• Superconformal Symmetry and Correlation Functions
• N=1 Superconformal Symmetry in Four Dimensions
• Superconformal Symmetry in Three-dimensions
• Superconformal Symmetry in Six-dimensions and Its Reduction to Four
• Bootstrapping the Minimal 3D SCFT
• Superspace formulation and correlation functions of 3d superconformal field theories
• Relation between parity-even and parity-odd CFT correlation functions in three dimensions
• Implications of N=4 superconformal symmetry in three spacetime dimensions
• Mixed three-point functions of conserved currents in three-dimensional superconformal field theory
• Implications of N=5, 6 superconformal symmetry in three spacetime dimensions
• Correlation functions in $\mathcal{N}=2$ Supersymmetric vector matter Chern-Simons theory
• Three-point functions of a superspin-2 current multiplet in 3D, N=1 superconformal theory
• On superconformal Chern-Simons-matter theories in N=4 superspace

Cited by in corpus (7)

• Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins
• Mapping Large N Slightly Broken Higher Spin (SBHS) theory correlators to Free theory correlators
• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Grassmann-odd three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT
• Three-point functions of higher-spin supercurrents in 4D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories