Invariant Regularization of Anomaly-Free Chiral Theories

TL;DR

This paper extends the invariant regularization scheme for chiral fermion theories in curved spacetime, ensuring gauge and Lorentz invariance, and is suitable for studying interactions involving all four fundamental forces in a chiral framework.

Contribution

It generalizes the Frolov-Slavnov regularization to include local Lorentz invariance and applies to arbitrary anomaly-free chiral theories, without introducing spectator fields.

Findings

The scheme preserves gauge and Lorentz invariance in chiral theories.

It is compatible with all four fundamental interactions in a chiral context.

Anomalous theories exhibit divergences not regularized by this scheme.

Abstract

We present a generalization of the Frolov-Slavnov invariant regularization scheme for chiral fermion theories in curved spacetimes. local gauge symmetries of the theory, including local Lorentz invariance. The perturbative scheme works for arbitrary representations which satisfy the chiral gauge anomaly and the mixed Lorentz-gauge anomaly cancellation conditions. Anomalous theories on the other hand manifest themselves by having divergent fermion loops which remain unregularized by the scheme. Since the invariant scheme is promoted to also include local Lorentz invariance, spectator fields which do not couple to gravity cannot be, and are not, introduced. Furthermore, the scheme is truly chiral (Weyl) in that all fields, including the regulators, are left-handed; and only the left-handed spin connection is needed. The scheme is, therefore, well suited for the study of the interaction of matter with all four known forces in a completely chiral fashion. In contrast with the vectorlike formulation, the degeneracy between the Adler-Bell-Jackiw current and the fermion number current in the bare action is preserved by the chiral regularization scheme.