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

Abstract

Abstract: For N$$ \mathcal{N} $$-extended superconformal field theories in three spacetime dimensions (3D), with 1 ≤ N$$ \mathcal{N} $$ ≤ 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$$ \mathcal{N}=1 $$ and N=3$$ \mathcal{N}=3 $$ cases. The specific feature of the N=2$$ \mathcal{N}=2 $$ 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 × S 2 and its universal covering space ℝ× S2 $$ \mathrm{\mathbb{R}}\times {S}^2 $$.