Some aspects of self-duality and generalised BPS theories

TL;DR

This paper explores a generalized self-duality concept in scalar field theories, enabling the construction of new solitons across dimensions and relating solutions with different topological features.

Contribution

It introduces a generalized self-duality framework that broadens the construction and relation of BPS solitons in various dimensions.

Findings

Infinite related BPS theories can be generated from a given scalar field theory.

The framework allows for the construction of new solitons in higher dimensions.

Field transformations relate solitons with different topological properties.

Abstract

If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related BPS equations. We point out that this fact may be understood as a simple consequence of an appropriately generalised notion of self-duality. We show that this self-duality framework enables us to generalize to higher dimensions the construction of new solitons from already known solutions. By performing simple field transformations our procedure allows us to relate solitons with different topological properties. We present several interesting examples of such solitons in two and three dimensions.