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

TL;DR

This paper presents a lower-dimensional action inspired by Kaluza-Klein theory that captures the dynamics and anomalies of chiral p-forms, including their massless and massive modes, gauge invariance, and supersymmetry consistency.

Contribution

It introduces a novel Kaluza-Klein inspired action for chiral p-forms that incorporates their anomalies and gauge invariance mechanisms, extending previous models.

Findings

Massless modes are (p-1)-forms with standard kinetic and Chern-Simons couplings.

Massive modes are p-forms charged under the Kaluza-Klein vector with parity-odd kinetic terms.

Generated Chern-Simons terms are consistent with anomalies and supersymmetry in 6D supergravity.

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 Stueckelberg-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.