The BPS property and its breaking in 1+1 dimensions

TL;DR

This paper demonstrates that the BPS property is a common feature in (1+1)-dimensional field theories, including higher-derivative models, and explores how impurities can break or preserve this property.

Contribution

It extends the understanding of BPS solutions to higher-derivative scalar field theories and analyzes impurity effects on the BPS property in these models.

Findings

BPS solutions are generic in higher-derivative scalar theories.

The BPS property can be preserved under specific impurity couplings.

Impurities can break or partially preserve the BPS property.

Abstract

We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which i) obey a lower-order Bogomolny-type equation in addition to the Euler-Lagrange equation, ii) have an energy which only depends on a topological charge and the global properties of the fields, but not on the local behaviour (coordinate dependence) of the solution, and iii) have zero pressure density. Concretely, to accomplish this program we study the existence of BPS solutions in field theories where the action functional (or energy functional) depends on higher than first derivatives of the fields. We find that that the existence of BPS solutions is a rather generic property of these higher-derivative scalar field theories. Hence, the BPS property in 1+1 dimensions can be extended not only to an arbitrary number of scalar fields and k-deformed models, but also to any (well behaved) higher derivative theory. We also investigate the possibility to destroy the BPS property by adding an impurity which breaks the translational symmetry. Further, we find that there is a particular impurity-field coupling which still preserves {\it one-half} of the BPS-ness. An example of such a BPS kink-impurity bound state is provided.