Hyperbolic deformation of a gauge field theory and the hierarchy problem

TL;DR

This paper introduces a hypercomplex gauge theory deformation with a parameter that creates a mass hierarchy without brane separation, revealing dualities and a flow resembling QED charge renormalization.

Contribution

It proposes a novel hypercomplex deformation of a U(1) gauge theory that naturally generates a hierarchy and uncovers dualities between interaction regimes.

Findings

Revealed a duality between real and hybrid potential parts.

Established a flow for electromagnetic coupling mimicking QED renormalization.

Demonstrated a mechanism for hierarchy generation without brane stabilization.

Abstract

The problem of the gauge hierarchy is brought up in a hypercomplex scheme for a U(1) field theory; in such a scheme a compact gauge group is deformed through a \gamma-parameter that varies along a non-compact internal direction, transverse to the U(1) compact one, and thus an additional SO(1,1) gauge symmetry is incorporated. This transverse direction can be understood as an extra internal dimension, which will control the spontaneous symmetry breakdown, and will allow us to establish a mass hierarchy. In this mechanism there is no brane separation to be stabilized as in the braneworld paradigm, however, a different kind of fine-tuning is needed in order to generate the wished electroweak/Planck hierarchy. By analyzing the effective self-interactions and mass terms of the theory, an interesting duality is revealed between the real and hybrid parts of the effective potential. This duality relates the weak and strong self-interaction regimes of the theory, due to the fact that both mass terms and self-coupling constants appear as one-parameter flows in \gamma. Additionally the \gamma-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.