Supersymmetric AdS(5) solutions of massive IIA supergravity

Abstract

Motivated by a recently found class of AdS(7) solutions, we classify AdS(5) 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 AdS(7) 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 Sigma(g). The ratio of their free energy coefficients is proportional to the Euler characteristic of Sigma(g). As a byproduct, we also find the analytic expression for the AdS(7) 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.