Non-Abelian electric-magnetic duality with supersymmetry in 4D and 10D

@article{Nishino2015NonAbelianED,
  title={Non-Abelian electric-magnetic duality with supersymmetry in 4D and 10D},
  author={H Nishino and Subhash Rajpoot},
  journal={Physical Review D},
  year={2015},
  volume={92},
  pages={085014}
}
We present electric-magnetic (Hodge) duality formulation for non-Abelian gauge groups with N=1 supersymmetry in 3+1 (4D) dimensions. Our system consists of three multiplets: (i) A super-Yang-Mills vector multiplet (YMVM) $(A_\mu{}^I, \lambda^I)$, (ii) a dual vector multiplet (DVM) $(B_\mu{}^I, \chi^I)$, and (iii) an unphysical tensor multiplet (TM) $(C_{\mu\nu}{}^I, \rho^I, \varphi^I)$, with the index I for adjoint representation. The multiplets YMVM and DVM are dual to each other like: $G_{\mu… 

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