Localizing Romans supergravity

Abstract: We derive a general formula for the on-shell action of six-dimensional Euclidean Romans supergravity using equivariant localization. Our results are obtained without the need for solving any of the equations of motion, instead working on the assumption of the existence of a solution. We show that the on-shell action is completely determined in terms of the R-symmetry Killing vector and topological data. We easily recover known results in the literature, make predictions for hitherto unknown solutions, and also match to holographic field theory duals.