Gödel spacetimes, Abelian instantons, the graviphoton background and other flacuum solutions Original Research Article

We study the relations between all the vacua of Lorentzian and Euclidean d=4,5,6 SUGRAs with 8 supercharges, finding a new limiting procedure that takes us from the over-rotating near-horizon BMPV black hole to the Gödel spacetime. The timelike compactification of the maximally supersymmetric Gödel solution of N=1, d=5 SUGRA gives a maximally supersymmetric solution of pure Euclidean N=2, d=4 with flat space but non-trivial anti-selfdual vector field flux (flacuum) that, on the one hand, can be interpreted as an U(1) instanton on T4 and that, on the other hand, coincides with the graviphoton background shown by Berkovits and Seiberg to produce the C-deformation introduced recently by Ooguri and Vafa. We construct flacuum solutions in other theories such as Euclidean type IIA supergravity.