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Durham University

Department of Mathematical Sciences

Staff

Publication details for Professor Emeritus Wojtek Zakrzewski

Ferreira, L. A., Klimas, P. & Zakrzewski, Wojtek J. (2019). Self-dual sectors for scalar field theories in (1 + 1) dimensions. Journal of High Energy Physics 2019(1): 20.

Author(s) from Durham

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.