TY - JOUR

T1 - Superconformal field theory in three dimensions: correlation functions of conserved currents

AU - Buchbinder, Evgeny

AU - Kuzenko, Sergei M

AU - Samsonov, Igor

PY - 2015/6/22

Y1 - 2015/6/22

N2 - © 2015, The Author(s). 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 S1× S2 and its universal covering space ℝ×S2$$ \mathrm{\mathbb{R}}\times {S}^2 $$.

AB - © 2015, The Author(s). 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 S1× S2 and its universal covering space ℝ×S2$$ \mathrm{\mathbb{R}}\times {S}^2 $$.

U2 - 10.1007/JHEP06(2015)138

DO - 10.1007/JHEP06(2015)138

M3 - Article

SN - 1029-8479

VL - 2015

SP - 1

EP - 71

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 6

ER -