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.
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In pure N=4 Poincaré supergravity, all extremal spherically symmetric attractors (constant or non-constant moduli) preserve 1/4 supersymmetry for generic charges with I4>0; non-BPS attractors cannot occur.
Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.
citing papers explorer
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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.
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Supersymmetry and Attractors in N = 4 Supergravity: The Superconformal Approach
In pure N=4 Poincaré supergravity, all extremal spherically symmetric attractors (constant or non-constant moduli) preserve 1/4 supersymmetry for generic charges with I4>0; non-BPS attractors cannot occur.
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On anomaly free 4d $\mathcal{N}$=4 and 6d (2,0) conformal supergravities and UV finiteness of Poincar\'e supergravities
Anomaly cancellation for specific multiplet numbers in conformal supergravities implies divergences proportional to n_v+2 in 4d PSG and n_T-21 in 6d PSG.