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

TL;DR

We develop a Kaluza-Klein inspired, parity-violating action for chiral $p$-forms in $D=2p+2$ with even $p$, obtained by circle reduction and incorporating the self-duality constraint at the $(D-1)$-dimensional level. Massless zero modes become $(p-1)$-forms with standard kinetics and KK-vector couplings, while massive KK modes appear as parity-odd, gauged $p$-forms with masses $m_n = c\, n\, r^{-1}$; these modes couple through a Chern-Simons structure to the KK vector. A one-loop calculation of the five-dimensional KK Chern-Simons coupling $k_{ m cs}$ from the tower of chiral fields reproduces the higher-dimensional anomaly data, yielding $k_{ m cs} = 9 - T$ for $(1,0)$ theories and $k_{ m cs}=0$ for $(2,0)$ theories, in agreement with gravitational anomaly cancellation and SUSY constraints. The framework thus links lower-dimensional Chern-Simons terms to higher-dimensional anomalies and offers a tool applicable to other duality-constrained systems.

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.

Figures (1)

• Figure 1: Diagrams contributing to $\langle A^0 A^0 A^0 \rangle$.