Supersymmetric AdS_5 solutions of massive IIA supergravity

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 CFT_6 and CFT_4 are related by twisted compactification on a Riemann surface $Σ_g$. The ratio of their free energy coefficients is proportional to the Euler characteristic of $Σ_g$. 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.

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