Supersymmetric Calculation of Mixed KäHLER-Gauge and Mixed KäHLER-Lorentz Anomalies

Abstract

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 ${\cal R}^2$ 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 $Z_N$ orbifolds.