On Lorentz Invariant Actions for Chiral P-Forms

TL;DR

The paper addresses the long-standing problem of constructing manifest Lorentz-invariant actions for chiral p-forms in $D=2(p+1)$ and clarifies the relationship between an infinite-tail auxiliary-field formulation and a minimal nonpolynomial formulation with a single auxiliary scalar $a$. Through a detailed Hamiltonian analysis, it shows that the nonpolynomial action has a simple, quadratic canonical Hamiltonian and Dirac constraints that are all first class, describing a single chiral p-form, unlike the Siegel model. For the $d=2$ chiral scalar case, the authors demonstrate a twisting of the first-class constraint that can cancel the quantum central charge, suggesting a possible absence of anomaly in an appropriate quantum version; for $D=6$ chiral 2-forms the framework yields a covariant Hamiltonian structure with only first-class constraints. The work further suggests that the framework can couple to gravity covariantly, may accommodate supersymmetric extensions, and provides a controlled path toward consistent truncations and anomaly-free quantization of chiral p-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 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.