Chern–Simons D=3D=3, N=6N=6 superfield theory

We construct the D=3,N=5D=3,N=5 harmonic superspace using the SO(5)/U(1)×U(1)SO(5)/U(1)×U(1) harmonics. Three gauge harmonic superfields satisfy the off-shell constraints of the Grassmann and harmonic analyticities. The corresponding component supermultiplet contains the gauge field AmAm and an infinite number of bosonic and fermionic fields with the SO(5)SO(5) vector indices arising from decompositions of gauge superfields in harmonics and Grassmann coordinates. The non-Abelian superfield Chern–Simons action is invariant with respect to the N=6N=6 superconformal supersymmetry realized on the N=5N=5 superfields. The component Lagrangian contains the Chern–Simons interaction of AmAm and an infinite number of bilinear and trilinear interactions of auxiliary fields. The fermionic and bosonic auxiliary fields from the infinite N=5N=5 multiplet vanish on-shell.