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Self-dual sectors for scalar field theories in (1 + 1) dimensions
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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.
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Further comments on BPS systems
In a two-field BPS sine-Gordon model, static soliton solutions are numerically shown to exhibit very slow attraction or repulsion caused by numerical noise exciting extra zero modes.
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