A Kaluza–Klein inspired action for chiral p-forms and their anomalies

Abstract

The dynamics of chiral p-forms can be captured by a lower-dimensional parity-violating action motivated by a Kaluza–Klein reduction on a circle. The massless modes are (p−1)-forms with standard kinetic terms and Chern–Simons couplings to the Kaluza–Klein vector of the background metric. The massive modes are p-forms charged under the Kaluza–Klein vector and admit parity-odd first-order kinetic terms. Gauge invariance is implemented by a Stückelberg-like mechanism using (p−1)-forms. A Chern–Simons term for the Kaluza–Klein vector is generated at one loop by massive p-form modes. These findings are shown to be consistent with anomalies and supersymmetry for six-dimensional supergravity theories with chiral tensor multiplets.