Self-dual sectors for scalar field theories in (1 + 1) dimensions

Abstract

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.

39 pages, 17 figures

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• Spectral walls in multifield kink dynamics
• Asymmetric kink scattering in a two-component scalar field theory model
• Spectral Walls at One Loop
• Wobbling kinks in a two-component scalar field theory: Interaction between shape modes
• Kink scattering in a generalized Wess-Zumino model
• Asymmetric scattering between kinks and wobblers
• Compact kink and its interaction with compact oscillons
• A Generalised Self-Duality for the Yang-Mills-Higgs System
• Extended multi-scalar field theories in (1+1) dimensions
• Moduli space with a boundary
• BPS states for scalar field theories based on ${\mathfrak{g}}_2$ and $\mathfrak{su}(4)$ algebras