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$$ \mathcal{N} $$ = 3 nonlinear multiplet and supergravity
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DOI：10.1007/JHEP07(2025)262.png)
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Abstract
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We propose an $$ \mathcal{N} $$ = 3 nonlinear multiplet coupled to conformal supergravity and use it to formulate the equations of motion for $$ \mathcal{N} $$ = 3 Poincaré supergravity. These equations, which are naturally described in a new curved supergeometry with structure group SL(2, ℂ), imply that the $$ \mathcal{N} $$ = 3 super-Bach tensor vanishes, and thus every solution of Poincaré supergravity is a solution of conformal supergravity. The aforementioned superspace formulation, which we refer to as $$ \mathcal{N} $$ = 3 Einstein superspace, is described in terms of two dimension-1/2 superfields: (i) the super-Weyl spinor Wα; and (ii) a spinor isospinor $$ {\chi}_{\alpha}^i $$ .
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