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

TL;DR

This paper develops a method to construct scalar field theories in (1+1) dimensions with exact self-dual solutions using Lie group representation theory, leading to models with rich topological structures.

Contribution

It introduces a novel algebraic approach to generate self-dual sectors in scalar field theories via a pre-potential based on Lie group representations.

Findings

Constructed explicit self-dual solutions for SU(2), SU(3), and SO(5) models.

Demonstrated the existence of infinite degenerate vacua and topologically non-trivial solutions.

Provided a framework for analyzing self-duality in scalar field theories using algebraic methods.

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.