### 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}$$ \mathrm{\mathbb{R}}\times {S}^2 $$.

Original language | English |
---|---|

Article number | 138 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 6 |

DOIs | |

Publication status | Published - 26 Jun 2015 |

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### Keywords

- Extended Supersymmetry
- Superspaces

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2015*(6), [138]. https://doi.org/10.1007/JHEP06(2015)138

**Superconformal field theory in three dimensions : correlation functions of conserved currents.** / Buchbinder, Evgeny I.; Kuzenko, Sergei M.; Samsonov, Igor B.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2015, no. 6, 138. https://doi.org/10.1007/JHEP06(2015)138

}

TY - JOUR

T1 - Superconformal field theory in three dimensions

T2 - correlation functions of conserved currents

AU - Buchbinder, Evgeny I.

AU - Kuzenko, Sergei M.

AU - Samsonov, Igor B.

PY - 2015/6/26

Y1 - 2015/6/26

N2 - 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 - 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$$ \mathrm{\mathbb{R}}\times {S}^2 $$.

KW - Extended Supersymmetry

KW - Superspaces

UR - http://www.scopus.com/inward/record.url?scp=84932607445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84932607445&partnerID=8YFLogxK

U2 - 10.1007/JHEP06(2015)138

DO - 10.1007/JHEP06(2015)138

M3 - Article

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 6

M1 - 138

ER -