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

  • L. A. FerreiraEmail author
  • P. Klimas
  • Wojtek J. Zakrzewski
Open Access
Regular Article - Theoretical Physics


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.


Integrable Field Theories Integrable Hierarchies Solitons Monopoles and Instantons 


Open Access

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.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Instituto de Física de São Carlos, IFSC/USPUniversidade de São PauloSão CarlosBrazil
  2. 2.Universidade Federal de Santa CatarinaFlorianópolisBrazil
  3. 3.Department of Mathematical SciencesUniversity of DurhamDurhamU.K.

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