Nonintegrability of self-dual Yang–Mills–Higgs system

2006/05/31 by Takeo Inami, Shie Minakami, Muneto Nitta
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2006.06.015

published as Nucl.Phys.B752:391-403,2006 · 15 pages, no figures, v2: references added, v3: typos corrected, the final version to appear in NPB

arxiv created 2006/06/28 · openalex publication_date 2006/07/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We examine integrability of self-dual Yang-Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painleve property. This fact suggests that these equations are not integrable.

Citations

• Instantons in the Higgs phase
• Non-commutative Ward's conjecture and integrable systems
• Non-Abelian vortices on a cylinder: Duality between vortices and walls
• Construction of Non-Abelian Walls and their Complete Moduli Space
• ArbitraryN-vortex solutions to the first order Ginzburg-Landau equations
• Global structure of moduli space for BPS walls
• Non-Abelian walls in supersymmetric gauge theories
• TASI Lectures on Solitons
• All exact solutions of a1/4Bogomol’nyi-Prasad-Sommerfield equation