Chern–Simons theory in the $SO(5)/U(2)$ harmonic superspace

We consider the superspace of $D=3$, $N=5$ supersymmetry using $SO(5)/U(2)$ harmonic coordinates. Three analytic $N=5$ gauge superfields depend on three vector and six harmonic bosonic coordinates and also on six Grassmann coordinates. Decomposing these superfields in Grassmann and harmonic coordinates yields infinite-dimensional supermultiplets including a three-dimensional gauge Chern–Simons field and auxiliary bosonic and fermionic fields carrying $SO(5)$ vector indices. The superfield action of this theory is invariant with respect to the $D=3$, $N=6$ conformal supersymmetry realized on $N=5$ superfields.