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

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. Th...

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Bibliographic Details
Published in:arXiv.org 2020-09
Main Authors: Hamanaka, Masashi, Shan-Chi, Huang
Format: Article
Language:English
Subjects:
Density
Domain walls
Euclidean geometry
Mathematical analysis
Solitary waves
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.09248