Flat spacetime is the only fully supersymmetric solution in four-dimensional N=3 and N=4 higher derivative Poincaré supergravity, unlike N=2 where Bertotti-Robinson geometry also qualifies.
The $\mathcal{N}=3$ Weyl Multiplet in Four Dimensions
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abstract
The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for $\mathcal{N}=3$, $D = 4$. The construction is based on a supersymmetry truncation from the $\mathcal{N}=4$ Weyl multiplet, on coupling with a current multiplet, and on the implementation of a soft algebra at the nonlinear level, extending su$(2, 2|3)$. This is the first step towards a superconformal calculus for $\mathcal{N}=3$, $D = 4$.
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Only Flat Spacetime is Full BPS in Four Dimensional N=3 and N=4 Supergravity
Flat spacetime is the only fully supersymmetric solution in four-dimensional N=3 and N=4 higher derivative Poincaré supergravity, unlike N=2 where Bertotti-Robinson geometry also qualifies.