Chiral tensor fields and spontaneous breaking of Lorentz symmetry

TL;DR

This paper explores how antisymmetric tensor fields interacting with matter could lead to spontaneous Lorentz symmetry breaking, driven by quantum fluctuations of the top quark, with implications for the gauge hierarchy problem.

Contribution

It calculates the one-loop beta function for a quartic self-interaction of chiral antisymmetric tensor fields, suggesting possible Lorentz symmetry breaking.

Findings

Top quark fluctuations drive the coupling negative at low scales

Potential spontaneous Lorentz symmetry breaking indicated

Further tensor loop calculations needed for confirmation

Abstract

Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.