Supersymmetric calculation of mixed Kähler-gauge and mixed Kähler-Lorentz anomalies (Q1967704)

We present a manifestly supersymmetric procedure for calculating the contributions from matter loops to the mixed Kähler-gauge and to the mixed Kähler-Lorentz anomalies in \(N=1\), \(D=4\) supergravity-matter systems. We show how this procedure leads to the well-known result for the mixed Kähler-gauge anomaly. For general supergravity-matter systems the mixed Kähler-Lorentz anomaly is found to contain a term proportional to \(R^{2}\) with a background field dependent coefficient as well as terms proportional to \((C_{mnpq})^{2}\) and to the Gauss-Bonnet topological density. We briefly comment on the relationship between the mixed Kähler-Lorentz anomaly and the moduli dependent threshold corrections to gravitational couplings in \(\mathbb{Z}_{\mathbb{N}}\) orbifolds.