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

Evgeny I. Buchbinder, Sergei M. Kuzenko, Igor B. Samsonov

Research output: Contribution to journalArticle

18 Citations (Scopus)

### 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 S1× S2 and its universal covering space ℝ×S2$$\mathrm{\mathbb{R}}\times {S}^2$$.

Original language English 138 Journal of High Energy Physics 2015 6 https://doi.org/10.1007/JHEP06(2015)138 Published - 26 Jun 2015

### Fingerprint

fine structure
Minkowski space
conservation equations
correlators
supergravity
supersymmetry
constrictions
coverings
symmetry
coefficients

### Keywords

• Extended Supersymmetry
• Superspaces

### ASJC Scopus subject areas

• Nuclear and High Energy Physics

### Cite this

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

In: Journal of High Energy Physics, Vol. 2015, No. 6, 138, 26.06.2015.

Research output: Contribution to journalArticle

Buchbinder, Evgeny I. ; Kuzenko, Sergei M. ; Samsonov, Igor B. / Superconformal field theory in three dimensions : correlation functions of conserved currents. In: Journal of High Energy Physics. 2015 ; Vol. 2015, No. 6.
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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$$\mathrm{\mathbb{R}}\times {S}^2$$.

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