Classical solitons in anti-self-dual Yang-Mills theory
Abstract
We study classical soliton solutions in split-signature anti-self-dual Yang-Mills theory. Using Zakharov's dressing method, we construct rational lump solitons, which are localised near two-dimensional surfaces, and wall solitons, which have codimension one. We further describe multi-phase solutions which have multiple walls meeting at trivalent junctions and form four-dimensional foam-like structures. Two-pole solutions describe soliton interactions and we find non-trivial colour-dressed phase shifts for wall interactions. We consider the four-dimensional analogue of Ward's lump scattering for the restricted kinematics of coincident poles and show that there are non-trivial interactions in the collinear limit. Finally, we show that the determinant of the soliton matrix provides a τ-function which acts as a potential for gauge-invariant scalar quantities such as the Yang-Mills Lagrangian density.
Related
- Expansion attractor in classical Yang-Mills theory
- On equivalence between solution structures of the anti-self-dual Yang--Mills equations
- Realization of several related (2+1)-dimensional integrable systems via an anti-self-dual Yang--Mills reduction
- Solitons in the nonlinear Schrödinger equation with the pseudo-Raman term, anti-diffusion gain and nonlinear loss
- One-loop unifying relations between Yang-Mills theory and the nonlinear sigma model from Berends-Giele currents
BibTeX
@misc{mcloughlin2026classical,
title = {{Classical solitons in anti-self-dual Yang-Mills theory}},
author = {Tristan McLoughlin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27074},
eprint = {2610.27074},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27074},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Classical solitons in anti-self-dual Yang-Mills theory
AU - Tristan McLoughlin
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.27074
UR - https://arxiv.org/abs/2610.27074
AB - We study classical soliton solutions in split-signature anti-self-dual Yang-Mills theory. Using Zakharov's dressing method, we construct rational lump solitons, which are localised near two-dimensional surfaces, and wall solitons, which have codimension one. We further describe multi-phase solutions which have multiple walls meeting at trivalent junctions and form four-dimensional foam-like structures. Two-pole solutions describe soliton interactions and we find non-trivial colour-dressed phase shifts for wall interactions. We consider the four-dimensional analogue of Ward's lump scattering for the restricted kinematics of coincident poles and show that there are non-trivial interactions in the collinear limit. Finally, we show that the determinant of the soliton matrix provides a τ-function which acts as a potential for gauge-invariant scalar quantities such as the Yang-Mills Lagrangian density.
ER -