Least-Order Torsion-Gravity for Chiral-Spinor Fields, induced Self-Interacting Potentials and Parity Conservation

TL;DR

This paper investigates the most general torsion-inclusive gravitational action with chiral spinor fields, deriving effective self-interacting potentials that surprisingly conserve parity despite initial parity-odd contributions.

Contribution

It introduces a comprehensive analysis of torsion in gravity coupled with chiral spinors, deriving parity-conserving self-interactions from a general parity-inclusive action.

Findings

Effective potentials are parity conserving despite initial parity-odd terms

Decomposition of torsion yields self-interacting chiral fermion terms

General least-order derivative action encompasses all parity contributions

Abstract

We will consider the most general least-order derivative action for the torsional completion of gravitational backgrounds filled with left-handed and right-handed semi-spinorial fields, accounting for all parity-even as well as parity-odd contributions; we will proceed by performing the customary analysis, decomposing torsion and substituting it in terms of the semi-spinorial density currents, in order to obtain the effective action with the torsionally-induced self-interacting potentials among the chiral fermionic fields: we shall see that the resulting effective non-linear potentials will turn eventually out to be parity conserving after all.