Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

Area of Science:

• Theoretical Physics
• High Energy Physics
• Cosmology

Background:

• Investigating non-perturbative aspects of quantum field theories in curved spacetime.
• Understanding the behavior of Yang-Mills theory on de Sitter space (dS4) is crucial for cosmology and early universe models.

Purpose of the Study:

• To construct and analyze smooth, spatially homogeneous magnetic solutions for pure SU(2) Yang-Mills theory on dS4.
• To explore the properties of these solutions, including their energy and action.

Main Methods:

• Utilized a slicing of dS4 into R×S3 and an SU(2)-equivariant ansatz.
• Reduced the Yang-Mills equations to ordinary matrix differential equations, mapping them to Newtonian dynamics in a double-well potential.
• Analyzed solutions arising from the local maximum of the potential and the double-well bounce.

Main Results:

• Constructed a specific magnetic solution with the color-magnetic field B[over ˜]_{a}=-1/2I_{a}/(R^{2}cosh^{2}τ).
• Demonstrated that these spatially homogeneous configurations possess finite energy and finite action, with the action given by -1/2j(j+1)(2j+1)π³ in a spin-j representation.
• Identified a family of homogeneous finite-action electric-magnetic solutions and a continuum of solutions with vanishing energy and action.

Conclusions:

• The study successfully constructs novel, smooth, and homogeneous Yang-Mills solutions in de Sitter spacetime.
• These findings offer insights into non-perturbative quantum field theory in curved backgrounds.
• The existence of a continuum of solutions suggests a rich structure of the Yang-Mills theory on dS4.