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

We describe three analytic classes of infinitely many AdSd supersymmetric solutions of massive IIA supergravity, for d=7,5,4. The three classes are related by simple universal maps. For example, the AdS7×M3 solutions (where M3 is topologically S3) are mapped to AdS5×Σ2×M3′, where Σ2 is a Riemann surface of genus g≥2 and the metric on M3′ is obtained by distorting M3 in a certain way. The solutions can have localized D6 or O6 sources, as well as an arbitrary number of D8-branes. The AdS7 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 AdS4 solutions have numerical "attractor" generalizations that might be useful for flux compactification purposes.