Six-Dimensional Superconformal Theories and their Compactifications from Type IIA Supergravity

We describe three analytic classes of infinitely many AdS(d) supersymmetric solutions of massive IIA supergravity, for d=7,5,4. The three classes are related by simple universal maps. For example, the AdS(7)×M(3) solutions (where M(3) is topologically S(3)) are mapped to AdS(5)×Σ(2)×M(3)', where Σ(2) is a Riemann surface of genus g≥2 and the metric on M(3)' is obtained by distorting M(3) in a certain way. The solutions can have localized D6 or O6 sources, as well as an arbitrary number of D8-branes. The AdS(7) case (previously known only numerically) is conjecturally dual to an NS5-D6-D8 system. The field theories in three and four dimensions are not known, but their number of degrees of freedom can be computed in the supergravity approximation. The AdS(4) solutions have numerical "attractor" generalizations that might be useful for flux compactification purposes.