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$SU(4)$ harmonic superspace and supersymmetric gauge theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 269-289 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the harmonic superspace formalism in $N=4$ supersymmetry based on $SU(4)/SU(2)\times SU(2)\times U(1)$ harmonics, which was previously used in Abelian gauge theory. We propose a transformation of non-Abelian constraints in the standard $N{=}4$ superspace into a superfield equation for two basic analytic superfields: an independent strength $W$ of dimension one and a dimensionless harmonic four-prepotential $V$ of the $U(1)$ charge two. These constraint equations I explicitly depend on the Grassmann coordinates $\theta$, although they are covariant under nonstandard $N=4$ supersymmetry transformations. The component expansion of superfield equations I generates the known equations for physical fields of the $N=4$ supermultiplet, with the auxiliary fields vanishing or expressible in terms of physical fields on the mass shell. In the harmonic formalism of $N=4$ supergauge theory off the mass shell, we construct a gauge-invariant action $A(W,V)$ for two unconstrained non-Abelian analytic superfields $W$ and $V$; this action contains theta factors in each term and is invariant under the $SU(4)$ automorphism group and scaling transformations. At the level of component fields, this model acquires an interaction of two infinite-dimensional $N=4$ supermultiplets involving physical and auxiliary fields. The action $A(W,V)$ generates analytic equations of motion II, alternative to the superfield constraints I. Both sets of equations give equivalent equations for physical component fields of the $N=4$ gauge supermultiplet. We construct a nonlinear effective interaction for the Abelian harmonic superfield $W$.
Keywords: harmonic superspace, extended supersymmetry, Yang–Mills theory. 
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     title = {$SU(4)$ harmonic superspace and supersymmetric gauge theory},
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B. M. Zupnik. $SU(4)$ harmonic superspace and supersymmetric gauge theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 269-289. http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a5/

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