Parameter spaces of massive IIA solution

We find a new class of N = 2 massive IIA solutions whose internal spaces are S-2 fibrations over S-2 x S-2. These solutions appear naturally as massive deformations of the type IIA reduction of Sasaki-Einstein manifolds in M-theory, including Q(1,1,1) and Y-p,Y-k, and play a role in the AdS(4)/CFT3 correspondence. We use this example to initiate a systematic study of the parameter space of massive solutions with fluxes. We de fine and study the natural parameter space of the solutions, which is a certain dense subset of R-3, whose boundaries correspond to orbifold or conifold singularities. On a codimension-one subset of the parameter space, where the Romans mass vanishes, it is possible to perform a lift to M-theory; extending earlier work, we produce a family A(p,q,r) of Sasaki-Einstein manifolds with cohomogeneity one and SU(2) x SU(2) x U(1) isometry. We also propose Chern-Simons theory describing the duals of the massless and massive solutions.