Wrapped M5-branes and complex saddle points

Abstract

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>We study the effects of the introduction of a <jats:italic>ϑ</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:italic>M</jats:italic>2-branes, but is there in the case of <jats:italic>M</jats:italic>5-branes wrapping hyperbolic manifolds Σ<jats:sub>3</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 Σ<jats:sub>3</jats:sub>. This is consistent with the characteristics of the dual three-dimensional 𝒩= 2 SCFT predicted by the 3<jats:italic>d</jats:italic>-3<jats:italic>d</jats:italic> correspondence, and we match the large <jats:italic>N</jats:italic> limit of its partition functions in the known cases.</jats:p>