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

TL;DR

This paper demonstrates that integrating out massive Kaehler-Dirac fermions in three dimensions yields a topological Chern-Simons gravity theory, with anomaly cancellation via inflow and generalization to higher dimensions.

Contribution

It introduces a novel connection between Kaehler-Dirac fermions and topological gravity, extending the understanding of anomaly inflow in odd-dimensional spaces.

Findings

Effective action is a topological Chern-Simons gravity theory.

Anomaly inflow cancels gravitational anomalies on domain walls.

Results generalize to higher odd dimensions.

Abstract

We show that the effective action that results from integrating out massive Kaehler-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 Kaehler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are cancelled 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.