https://doi.org/10.1140/epjc/s10052-016-3944-9
Regular Article - Theoretical Physics
Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
1
Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570, Puebla, Pue., Mexico
2
Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Puebla, Apartado postal 1152, 72001, Puebla, Pue., Mexico
* e-mail: rcartas@ifuap.buap.mx
Received:
22
November
2015
Accepted:
11
February
2016
Published online:
25
February
2016
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 hypercomplex 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 hybrid potential with two real components, and with 
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 spontaneous symmetry breaking scenarios with running masses for the vectorial and scalar Higgs fields, and such as 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 hyperbolic electrodynamics does not admit topological defects associated with continuous symmetries.
© The Author(s), 2016
