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Manifest \( {\text{SO}}\left( \mathcal{N} \right) \) invariance and S-matrices of three-dimensional \( \mathcal{N} = 2,4,8 \) SYM

  • Abhishek Agarwal
  • Donovan Young
Article

Abstract

An on-shell formalism for the computation of S-matrices of SYM theories in three spacetime dimensions is presented. The framework is a generalization of the spinor-helicity formalism in four dimensions. The formalism is applied to establish the manifest \( {\text{SO}}\left( \mathcal{N} \right) \) covariance of the on-shell superalgebra relevant to \( \mathcal{N} = 2,4 \) and 8 SYM theories in d = 3. The results are then used to argue for the \( {\text{SO}}\left( \mathcal{N} \right) \) invariance of the S matrices of these theories: a claim which is proved explicitly for the four-particle scattering amplitudes. Recursion relations relating tree amplitudes of three-dimensional SYM theories are shown to follow from their four-dimensional counterparts. The results for the four-particle amplitudes are verified by tree-level perturbative computations and a unitarity based construction of the integrand corresponding to the leading perturbative correction is also presented for the \( \mathcal{N} = 8 \) theory. For \( \mathcal{N} = 8 \) SYM, the manifest SO(8) symmetry is used to develop a map between the color-ordered amplitudes of the SYM and superconformal Chern-Simons theories, providing a direct connection between on-shell observables of D2 and M2-brane theories.

Keywords

Supersymmetric gauge theory Gauge-gravity correspondence Extended Supersymmetry 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.American Physical SocietyRidgeU.S.A.
  2. 2.Niels Bohr InstituteCopenhagenDenmark

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