Communications in Mathematical Physics

, Volume 163, Issue 2, pp 257–291 | Cite as

A symmetric family of Yang-Mills fields

  • Lorenzo Sadun
Article

Abstract

We examine a family of finite energySO(3) Yang-Mills connections overS4, indexed by two real parameters. This family includes both smooth connections (when both parameters are odd integers), and connections with a holonomy singularity around 1 or 2 copies ofRP2. These singular YM connections interpolate between the smooth solutions. Depending on the parameters, the curvature may be self-dual, anti-self-dual, or neither. For the (anti)self-dual connections, we compute the formal dimension of the moduli space. For the non-self-dual connections we examine the second variation of the Yang-Mills functional, and count the negative and zero eigenvalues. Each component of the non-self-dual moduli space appears to consist only of conformal copies of a single solution.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Modulus Space 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Lorenzo Sadun
    • 1
  1. 1.Department of MathematicsUniversity of TexasAustinUSA

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