The particle spectra of parity-violating theories: A less radical approach and an upgrade of PSALTer

TL;DR

This paper introduces an efficient algorithm for computing the particle spectrum in parity-violating gravitational theories, addressing computational challenges and enhancing the PSALTer software to include these theories.

Contribution

It presents a novel algorithm for analyzing parity-violating tensor theories and upgrades the PSALTer software for broader applicability in gravitational model analysis.

Findings

Successfully tested on parity-indefinite Einstein-Cartan gravity

Identifies conditions for absence of massive ghosts

Propagates two healthy massive scalars

Abstract

Due to computational barriers, the effects of parity violation have so far been grossly neglected in gravitational model-building, leading to a serious gap in the space of prior models. We present a new algorithm for efficiently computing the particle spectrum for any parity-violating tensorial field theory. It allows to extract conditions for the absence of massive ghosts without resorting to any manipulation of radicals in cases where the particle masses are irrational functions of the Lagrangian coupling coefficients. We test it against several examples, among which is the most general parity-indefinite Einstein-Cartan/Poincar\'e gravity that propagates two healthy massive scalars (in addition to the massless graviton). Importantly, we upgrade the PSALTer software in the Wolfram Language to accommodate parity-violating theories. PSALTer is a contribution to the xAct project.