Skyrmions from instantons inside domain walls.

Area of Science:

• High-energy physics
• Theoretical physics
• Mathematical physics

Background:

• Atiyah and Manton previously outlined a method for approximating Skyrmion solutions using Yang-Mills instantons.
• Skyrmions are topological solitons with applications in nuclear physics and condensed matter.
• Gauge theories describe fundamental forces and particle interactions.

Purpose of the Study:

• To provide a dynamical realization of the Atiyah-Manton construction of Skyrmions.
• To investigate the relationship between domain walls in gauge theories and Skyrmion solutions.
• To explore the emergence of Skyrme model dynamics from a higher-dimensional gauge theory.

Main Methods:

• Utilizing a five-dimensional non-Abelian gauge theory with domain walls.
• Analyzing the behavior of Yang-Mills instantons within the core of these domain walls.
• Deriving the effective world volume theory of the domain wall.

Main Results:

• Demonstrated that domain walls in five-dimensional gauge theory can host Yang-Mills instantons.
• Showed that the world volume dynamics of the domain wall are described by the Skyrme model, including a four-derivative term.
• Identified these instantons as domain wall Skyrmions, providing a dynamical interpretation.

Conclusions:

• The study successfully connects instanton physics in gauge theories with Skyrmion phenomenology.
• Domain walls serve as a natural medium for realizing Skyrmion solutions dynamically.
• This work offers a novel perspective on the interplay between gauge theory and soliton physics.