On the Consistency of a Fermion-Torsion Effective Theory

TL;DR

This paper examines the theoretical consistency of an effective quantum field theory involving axial vectors and Dirac spinors, revealing significant issues that restrict the existence of propagating torsion fields at low energies.

Contribution

It analyzes the unitarity and renormalizability of a torsion-related effective theory, highlighting fundamental problems that challenge its viability.

Findings

Serious problems in Ward identities and divergences.

Torsion may exist as a string excitation but not as a propagating field.

Severe restrictions on low-energy propagating torsion due to quantization issues.

Abstract

We discuss the possibility to construct an effective quantum field theory for an axial vector coupled to a Dirac spinor field. A massive axial vector describes antisymmetric torsion. The consistency conditions include unitarity and renormalizability in the low-energy region. The investigation of the Ward identities and the one- and two-loop divergences indicate serious problems arising in the theory. The final conclusion is that torsion may exist as a string excitation, but there are very severe restrictions for the existence of a propagating torsion field, subject to the quantization procedure, at low energies.