Variant = (1,1) supergravity and (Minkowski) 4 × S 2 vacua

We construct the fermionic sector and supersymmetry transformation rules of a variant supergravity theory obtained by generalized Kaluza–Klein reduction from seven dimensions. We show that this model admits both (Minkowski) 4 × S 2 and (Minkowski) 3 × S 3 supersymmetric vacua. We perform a consistent Kaluza–Klein reduction on S 2 and obtain supergravity coupled to a vector multiplet, which can be consistently truncated to give rise to supergravity with a chiral multiplet.