Hyperbolic deformation of a gauge field theory and the hierarchy problem
arXiv:1612.04436 · doi:10.1142/S0217751X16501773
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 γ-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 γ. Additionally the γ-deformation will establish a flow for the electromagnetic coupling that mimics the renormalization group flow for the charge in QED.
arXiv comment34 pages in latex, 21 figures
References in corpus (13)
- A Large Mass Hierarchy from a Small Extra Dimension
- New Dimensions at a Millimeter to a Fermi and Superstrings at a TeV
- Modeling the fifth dimension with scalars and gravity
- Hierarchies without Symmetries from Extra Dimensions
- Instantons and seven-branes in type IIB superstring theory
- Considerations on the hyperbolic complex Klein-Gordon equation
- Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincare symmetry
- Five dimensional 2-branes from special Lagrangian wrapped M5-branes
- Wrapped M5-branes leading to five dimensional 2-branes
- Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
- Symplectic covariance of the N=2 hypermultiplets
- Split-complex representation of the universal hypermultiplet
- Hidden Gauge Symmetry in Holomorphic Models