On Lorentz Invariant Actions for Chiral P-Forms

TL;DR

This paper explores Lorentz covariant formulations of chiral p-forms, showing how a complex auxiliary field model relates to a simpler scalar auxiliary field model, with implications for quantum anomalies.

Contribution

It establishes a connection between two Lorentz covariant formulations of chiral p-forms and analyzes their Hamiltonian structure, highlighting differences from the Siegel model.

Findings

The nonpolynomial action has first-class Dirac constraints.

The Hamiltonian is quadratic and energy-defining.

A twisting procedure can eliminate quantum anomalies in d=2.

Abstract

We demonstrate how a Lorentz covariant formulation of the chiral p-form model in D=2(p+1) containing infinitely many auxiliary fields is related to a Lorentz covariant formulation with only one auxiliary scalar field entering a chiral p-form action in a nonpolynomial way. The latter can be regarded as a consistent Lorentz-covariant truncation of the former. We make the Hamiltonian analysis of the model based on the nonpolynomial action and show that the Dirac constraints have a simple form and are all of the first class. In contrast to the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines energy of a single chiral p-form. In the case of d=2 chiral scalars the constraint can be improved by use of `twisting' procedure (without the loss of the property to be of the first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to possible absence of anomaly in an appropriate quantum version of the model.