A uniqueness theorem for warped $N>16$ Minkowski backgrounds with fluxes

We demonstrate that warped Minkowski space backgrounds, Rn−1,1×wMd−n , n≥3 , that preserve strictly more than 16 supersymmetries in d=11 and type II d=10 supergravities and with fields which may not be smooth everywhere are locally isometric to the Rd−1,1 Minkowski vacuum. In particular, all such flux compactification vacua of these theories have the same local geometry as the maximally supersymmetric vacuum Rn−1,1×Td−n .