Lorentz-invariant actions for chiralp-forms

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 first class. In contrast with the Siegel model the constraints are not the square of second-class constraints. The canonical Hamiltonian is quadratic and determines the energy of a single chiral $p$-form. In the case of $D=2$ chiral scalars the constraint can be improved by use of a ``twisting'' procedure (without the loss of the property to be first class) in such a way that the central charge of the quantum constraint algebra is zero. This points to the possible absence of an anomaly in an appropriate quantum version of the model.