Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories

TL;DR

This paper explores hypercomplex gauge theories, revealing novel symmetry breaking phenomena and string defects, with potential implications for quantum interference detection methods.

Contribution

It introduces a hypercomplex formulation of Abelian gauge theories, uncovering new vacuum structures, symmetry breaking scenarios, and exact string defect solutions.

Findings

Hypercomplex electrodynamics exhibits spontaneous symmetry breaking with running masses.

Exact Aharonov-Bohm type string solutions are found in the hypercomplex framework.

Hyperbolic electrodynamics lacks topological defects in certain limits.

Abstract

Inspired by the appearance of split-complex structures in the dimensional reduction of string theory, and in the theories emerging as byproducts, we study the hyper-complex formulation of Abelian gauge field theories, by incorporating a new complex unit to the usual complex one. The hypercomplex version of the traditional Mexican hat potential associated with the $U(1)$ gauge field theory, corresponds to a {\it hybrid} potential with two real components, and with $U(1)\times SO(1,1)$ as symmetry group. Each component corresponds to a deformation of the hat potential, with the appearance of a new degenerate vacuum. Hypercomplex electrodynamics will show novel properties, such as the spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and the Aharonov-Bohm type strings defects as exact solutions; these topological defects may be detected only by quantum interference of charged particles through gauge invariant loop integrals. In a particular limit, the {\it hyperbolic} electrodynamics does not admit topological defects associated with continuous symmetries