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.

v3, 27 pages; a few typos corrected and a footnote added; final version published in EPJC (Particles and Fields)

References in corpus (1)

• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions

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