Quantization of chiral antisymmetric tensor fields

TL;DR

This paper explores the quantization of chiral antisymmetric tensor fields with chiral couplings, proposing a consistent interacting theory that could relate to electroweak symmetry breaking and massive spin-one particles.

Contribution

It demonstrates that interacting chiral antisymmetric tensor fields can be consistently quantized, unlike the free theory, and suggests their role in electroweak symmetry breaking.

Findings

Interacting theory is stable and consistent upon quantization.

Chiral couplings grow large, leading to spontaneous symmetry breaking.

Massive chiral tensors behave as stable massive spin-one particles.

Abstract

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry and a local mass term is forbidden by symmetry. The chiral couplings to the fermions are asymptotically free, opening interesting perspectives for a possible solution to the gauge hierarchy problem. We argue that the interacting theory for such fields can be consistently quantized, in contrast to the free theory which is plagued by unstable solutions. We suggest that at the scale where the chiral couplings grow large the electroweak symmetry is spontaneously broken and a mass term for the chiral tensors is generated non-perturbatively. Massive chiral tensors correspond to massive spin one particles that do not have problems of stability. We also propose an equivalent formulation in terms of gauge fields.