Induced topological gravity and anomaly inflow from Kähler-Dirac fermions in odd dimensions

We show that the effective action that results from integrating out massive Kähler-Dirac fermions propagating on a curved three-dimensional space is a topological gravity theory of Chern-Simons type. In the presence of a domain wall, massless, two-dimensional Kähler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are canceled via anomaly inflow from the bulk gravitational theory. We also study the invariance of the theory under large gauge transformations. The analysis and conclusions generalize straightforwardly to higher dimensions.