Spontaneous Hopf Fibration in the Two-Higgs-Doublet Model.

Area of Science:

• High Energy Physics
• Theoretical Physics
• Particle Physics

Background:

• The Standard Model (SM) describes fundamental particles and forces.
• Two Higgs Doublet Models (2HDM) extend the SM Higgs sector.
• Topological defects can arise in field theories.

Purpose of the Study:

• Investigate the topological structure of the Standard Model within 2HDM.
• Explore the implications of Higgs-family symmetries on topological solutions.
• Characterize monopole and vortex solutions and their properties.

Main Methods:

• Applying energetic considerations to enforce topological structures.
• Analyzing the Hopf fibration of the Standard Model topology.
• Finding and characterizing monopole and vortex solutions.

Main Results:

• Energetic constraints necessitate a Hopf fibration of the Standard Model topology in 2HDM with SO(3) or U(1) Higgs-family symmetry.
• Monopole and vortex solutions are identified and their properties characterized.
• A connection to Nambu's monopole solution is demonstrated.
• The breaking of U(1)_{EM} in defect cores suggests a nonzero photon mass.

Conclusions:

• Hopf fibration is a key topological feature in specific 2HDM potentials.
• The identified topological defects offer insights into particle physics beyond the Standard Model.
• The core physics of these defects may provide mechanisms for photon mass generation.