Supersymmetric Calculation of Mixed K\"{a}HLER-Gauge and Mixed K\"{a}HLER-Lorentz Anomalies

TL;DR

This paper develops a supersymmetric method to compute matter loop contributions to mixed Kähler-gauge and Kähler-Lorentz anomalies in N=1 supergravity, revealing detailed anomaly structures and their implications.

Contribution

It introduces a manifestly supersymmetric procedure for calculating mixed anomalies in supergravity-matter systems, providing new insights into their structure and background dependencies.

Findings

Reproduces the known mixed Kähler-gauge anomaly result.

Identifies a background-dependent ${ m R}^2$ term in the mixed Kähler-Lorentz anomaly.

Links the mixed Kähler-Lorentz anomaly to moduli-dependent threshold corrections.

Abstract

We present a manifestly supersymmetric procedure for calculating the contributions from matter loops to the mixed K\"{a}hler-gauge and to the mixed K\"{a}hler- Lorentz anomalies in $N=1, D=4$ supergravity-matter systems. We show how this procedure leads to the well-known result for the mixed K\"{a}hler-gauge anomaly. For general supergravity-matter systems the mixed K\"{a}hler-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 K\"{a}hler-Lorentz anomaly and the moduli dependent threshold corrections to gravitational couplings in $Z_N$ orbifolds.