Geodesic
Chern--Simons theory in the~$SO(5)/U(2)$ harmonic superspace
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 217-234

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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.
Keywords: harmonic superspace, extended supersymmetry, Chern–Simons theory. 
@article{TMF_2008_157_2_a4,
     author = {B. M. Zupnik},
     title = {Chern--Simons theory in the~$SO(5)/U(2)$ harmonic superspace},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {217--234},
     publisher = {mathdoc},
     volume = {157},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a4/}
}
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B. M. Zupnik. Chern--Simons theory in the~$SO(5)/U(2)$ harmonic superspace. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 2, pp. 217-234. http://geodesic.mathdoc.fr/item/TMF_2008_157_2_a4/