Supersymmetric AdS5 solutions of massive IIA supergravity

Motivated by a recently found class of AdS7 solutions, we classify AdS5 solutions in massive IIA, finding infinitely many new analytical examples. We reduce the general problem to a set of PDEs, determining the local internal metric, which is a fibration over a surface. Under a certain simplifying assumption, we are then able to analytically solve the PDEs and give a complete list of all solutions. Among these, one class is new and regular. These spaces can be related to the AdS7 solutions via a simple universal map for the metric, dilaton and fluxes. The natural interpretation of this map is that the dual CFT6 and CFT4 are related by twisted compactification on a Riemann surface Σg. The ratio of their free energy coefficients is proportional to the Euler characteristic of Σg. As a byproduct, we also find the analytic expression for the AdS7 solutions, which were previously known only numerically. We determine the free energy for simple examples: it is a simple cubic function of the flux integers.