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Lesley Sibner1, Robert Sibner2, Yisong Yang3

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This study establishes the existence of minimal action charge-N calorons by constructing N-vortex solutions. These solutions are based on Witten-type equations for the Abelian Higgs model, linking to self-dual Yang-Mills theory.

Keywords:
finite temperatureinstantonsnonlinear equationstopological invariants

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Area of Science:

  • Theoretical Physics
  • Mathematical Physics
  • Quantum Field Theory

Background:

  • Recent work connects SO(3)-symmetric, charge-N self-dual Yang-Mills calorons on hyperbolic space to N-vortex solutions.
  • Witten's study on multiple instantons provides a foundation for this connection.

Purpose of the Study:

  • To establish the existence of minimal action charge-N calorons.
  • To construct arbitrarily prescribed N-vortex solutions of Witten-type equations.

Main Methods:

  • Construction of N-vortex solutions for an Abelian Higgs model.
  • Utilizing Witten-type equations.

Main Results:

  • Successfully established the existence of minimal action charge-N calorons.
  • Demonstrated the construction of arbitrarily prescribed N-vortex solutions.

Conclusions:

  • The study confirms the link between N-vortex solutions and charge-N calorons.
  • Provides a method for constructing specific caloron solutions via vortex solutions.