Journal of High Energy Physics (Jan 2019)

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

  • L. A. Ferreira,
  • P. Klimas,
  • Wojtek J. Zakrzewski

DOI
https://doi.org/10.1007/JHEP01(2019)020
Journal volume & issue
Vol. 2019, no. 1
pp. 1 – 38

Abstract

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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.

Keywords