Superconformal field theory in three dimensions: Correlation functions of conserved currents

TL;DR

This paper computes and analyzes the structure of two- and three-point correlation functions of conserved currents in 3D superconformal field theories with N=1,2,3, revealing supersymmetry constraints and introducing a supertwistor construction for various spacetimes.

Contribution

It provides explicit forms of correlation functions for supercurrents and flavor currents in 3D superconformal theories, highlighting supersymmetry restrictions and a new supertwistor framework.

Findings

Three-point function of supercurrent is uniquely determined by symmetry.

For N=2, two independent structures exist for flavor current correlators.

New supertwistor construction for diverse 3D spacetimes introduced.

Abstract

For N-extended superconformal field theories in three spacetime dimensions (3D), with N=1,2,3, we compute the two- and three-point correlation functions of the supercurrent and the flavour current multiplets. We demonstrate that supersymmetry imposes additional restrictions on the correlators of conserved currents as compared with the non-supersymmetric case studied by Osborn and Petkou in hep-th/9307010. It is shown that the three-point function of the supercurrent is determined by a single functional form consistent with the conservation equation and all the symmetry properties. Similarly, the three-point function of the flavour current multiplets is also determined by a single functional form in the N=1 and N=3 cases. The specific feature of the N=2 case is that two independent structures are allowed for the three-point function of flavour current multiplets, but only one of them contributes to the three-point function of the conserved currents contained in these multiplets. Since the supergravity and super-Yang-Mills Ward identities are expected to relate the coefficients of the two- and three-point functions under consideration, the results obtained for 3D superconformal field theory are analogous to those in 2D conformal field theory. In addition, we present a new supertwistor construction for compactified Minkowski superspace. It is suitable for developing superconformal field theory on 3D spacetimes other than Minkowski space, such as S^1 x S^2 and its universal covering space R x S^2.