jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe study the effects of the introduction of a jats:italicϑ</jats:italic> term in minimal gauged supergravity in four dimensions. We show why this term is not present in supergravity duals of field theories arising on wrapped jats:italicM</jats:italic>2-branes, but is there in the case of jats:italicM</jats:italic>5-branes wrapping hyperbolic manifolds Σjats:sub3</jats:sub>, and compute the higher-derivative corrections. Having proved that the on-shell supergravity action of any supersymmetric solution can be expressed in terms of data from the fixed points of a Killing vector, we show that it is proportional to a complex topological invariant of Σjats:sub3</jats:sub>. This is consistent with the characteristics of the dual three-dimensional 𝒩= 2 SCFT predicted by the 3jats:italicd</jats:italic>-3jats:italicd</jats:italic> correspondence, and we match the large jats:italicN</jats:italic> limit of its partition functions in the known cases.</jats:p>