Non-Abelian Electric-Magnetic Duality with Supersymmetry in 4D and 10D

Abstract

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) $(C_{\mu \nu }{}^I,{\rho }^I,{\phi }^I)$, with the index I for adjoint representation. The multiplets YMVM and DVM are dual to each other like: $G_{\mu \nu }{}^I=(1/2){\epsilon }_{\mu \nu }{}^{\rho \sigma }{F}_{\rho \sigma }{}^I$. The TM is unphysical, but still plays an important role for establishing the total consistency of the system, based on recently-developed tensor-hierarchy formulation. We also apply this technique to non-Abelian electric-magnetic duality in 9+1 (10D) dimensions. The extra bosonic auxiliary field $K_{{\mu }_1\cdots {\mu }_6}$ in 10D is shown to play an important role for the closure of supersymmetry on fields.

17 pages, 0 figure

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