New Soliton Solutions of Anti-Self-Dual Yang-Mills equations

Abstract

We study exact soliton solutions of anti-self-dual Yang-Mills equations for $G=GL(2)$ in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density Tr$F_{\mu \nu }{F}^{\mu \nu }$ can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group $G=U(2)$ can be realized on our solition solutions or not is also discussed on each real space.

19 pages; Dedicated to the memory of Jon Nimmo; v2: minor changes, discussion on singularities added, version to appear in JHEP

References in corpus (1)

• Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations

Cited by in corpus (6)

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• Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields
• Solitons in Open N=2 String Theory
• Soliton Resonances in Four Dimensional Wess-Zumino-Witten Model