Three-point functions of conserved supercurrents in 3D $\mathcal{N}=1$ SCFT: general formalism for arbitrary superspins

Abstract

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $⟨{\mathbf{J}}_{s_1}^{}{\mathbf{J}}_{s_2}^{\prime }{\mathbf{J}}_{s_3}^{\prime \prime }⟩$, where ${\mathbf{J}}_{s_1}^{}$, ${\mathbf{J}}_{s_2}^{\prime }$ and ${\mathbf{J}}_{s_3}^{\prime \prime }$ are conserved higher-spin supercurrents with superspins $s_1$, $s_2$ and $s_3$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_i\le 20$; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.

54 pages; v2: minor corrections, references added. arXiv admin note: substantial text overlap with arXiv:2210.13135

References in corpus (1)

• Off-shell superconformal nonlinear sigma-models in three dimensions

Cited by in corpus (2)

• Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins
• Superspace invariants and correlators in 4d $\mathcal{N}=1$ superconformal field theories