Minkowski4×S2 solutions of IIB supergravity

We classify urn:x-wiley:00158208:media:prop201800006:prop201800006-math-0002 Minkowski4 solutions of IIB supergravity with an urn:x-wiley:00158208:media:prop201800006:prop201800006-math-0003 symmetry geometrically realized by an S2‐foliation in the remaining six dimensions. For the various cases of the classification, we reduce the supersymmetric system of equations to PDEs. These cases often accommodate systems of intersecting branes and half‐maximally supersymmetric AdS5, 6, 7 solutions when they exist. As an example, we analyze the AdS6 case in more detail, reducing the supersymmetry equations to a single cylindrical Laplace equation. We also recover an already known linear dilaton background dual to the (1, 1) Little String Theory (LST) living on NS5‐branes, and we find a new Minkowski5 linear dilaton solution from brane intersections. Finally, we also discuss some simple Minkowski4 solutions based on compact conformal Calabi‐Yau manifolds