Comments on Chiral p-Forms

TL;DR

This paper examines the topological conditions for splitting non-chiral p-forms into chiral components and explores Lorentz-invariant self-couplings of chiral p-forms, highlighting their consistency and coupling to gravity.

Contribution

It provides a detailed analysis of the topological constraints for chiral p-forms and clarifies the conditions for consistent Lorentz-invariant self-couplings.

Findings

Topological conditions determine when non-chiral p-forms split into chiral parts.

Extra topological degrees of freedom appear when splitting conditions are not met.

Lorentz-invariant self-couplings satisfy the Dirac-Schwinger condition, ensuring consistency.

Abstract

Two issues regarding chiral $p$-forms are addressed. First, we investigate the topological conditions on spacetime under which the action for a non-chiral $p$-form can be split as the sum of the actions for two chiral $p$-forms, one of each chirality. When these conditions are not met, we exhibit explicitly the extra topological degrees of freedom and their couplings to the chiral modes. Second, we study the problem of constructing Lorentz-invariant self-couplings of a chiral $p$-form in the light of the Dirac-Schwinger condition on the energy-momentum tensor commutation relations. We show how the Perry-Schwarz condition follows from the Dirac-Schwinger criterion and point out that consistency of the gravitational coupling is automatic.