A new N=3 Einstein superspace is built from a proposed nonlinear multiplet, and the resulting equations of motion reduce to chi=0, implying the N=3 super-Bach tensor vanishes.
Structure of N= 2 Supergravity,
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${\mathcal N}=3$ nonlinear multiplet and supergravity
A new N=3 Einstein superspace is built from a proposed nonlinear multiplet, and the resulting equations of motion reduce to chi=0, implying the N=3 super-Bach tensor vanishes.