Self-dual sectors for scalar field theories in (1 + 1) dimensions
- 30 Downloads
We use ideas of generalized self-duality conditions to construct real scalar field theories in (1 + 1)-dimensions with exact self dual sectors. The approach is based on a pre-potential U that defines the topological charge and the potential energy of these theories. In our algebraic method to construct the required pre-potentials we use the representation theory of Lie groups. This approach leads naturally to an infinite set of degenerate vacua and so to topologically non-trivial self-dual solutions of these models. We present explicit examples for the groups SU(2), SU(3) and SO(5) and discuss some properties of these solutions.
KeywordsIntegrable Field Theories Integrable Hierarchies Solitons Monopoles and Instantons
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- N.S. Manton and P. Sutcliffe, Topological solitons, Cambridge Monographs on Mathematical Physics, (2004).Google Scholar
- Y.M. Shnir, Topological and Non-Topological Solitons in Scalar Field Theories, Cambridge University Press (2018).Google Scholar
- W.J. Zakrzewski, Low Dimensional Sigma Models, Adam Hilger, (1989).Google Scholar
- M.J. Ablowitz and P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, Lond. Math. Soc. Lect. Note Ser. 149 (1991).Google Scholar