Parameter spaces of massive IIA solution

We find a new class of N = 2 massive IIA solutions whose internal spaces are S2 vibrations over S2 - S2. These solutions appear naturally as massive deformations of the type IIA reduction of Sasaki-Einstein manifolds in M-theory, including Q1;1;1 and Y p;k, and play a role in the AdS4/CFT3 correspondence. We use this example to initiate a systematic study of the parameter space of massive solutions with uxes. We dene and study the natural parameter space of the solutions, which is a certain dense subset of R3, 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 Ap;q;r of Sasaki-Einstein manifolds with cohomogeneity one and SU(2) SU(2) U(1) isometry. We also propose a Chern-Simons theory describing the duals of the massless and massive solutions. © SISSA 2011.