Abstract
We show that the Bogomol'nyi-Prasad-Sommerfield (BPS) property is a generic feature of all models in ($1+1$) dimensions that does not put any restriction on the action. Here, by BPS solutions we understand static solutions that (i) obey a lower-order Bogomolny-type equation in addition to the Euler-Lagrange equation, (ii) have an energy that only depends on a topological charge and the global properties of the fields, but not on the local behavior (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 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 that breaks the translational symmetry. Further, we find that there is a particular impurity-field coupling that still preserves one-half of the BPS-ness. An example of such a BPS kink-impurity bound state is provided.
Highlights
BPS-type theories play a prominent role in current theoretical physics, where they offer an analytical insight into the nontrivial mathematical structure of topological solitons [1,2]
A common feature sheared by all known BPS models is the property that a pertinent topological lower bound on the energy functional is saturated by solutions of lower-order, so-called Bogomolnyi equations [3,4], corresponding to a first integration of the full field equations
This goes beyond the scope of the present paper, it is interesting to notice that the Korteweg de Vries (KdV) equation can be partially put into the BPS framework, as well
Summary
BPS-type theories play a prominent role in current theoretical physics, where they offer an analytical insight into the nontrivial mathematical structure of topological solitons [1,2]. An arbitrary model based on any number of real scalar fields φa (where a 1⁄4 1..N) defining a target space metric GabðφÞ and involving only first spatial derivatives possesses a BPS sector with solutions saturating the corresponding Bogomolnyi equations. These formal BPS solutions are topological solitons (e.g., kinks) if the vacuum structure of the model allows for field configurations interpolating between different vacua. If a higher-derivative static energy functional is interpreted as the static limit of a Lorentz noninvariant field theory (e.g., with a standard kinetic term), this theory can, e.g., be viewed as the continuum limit of a one-dimensional discrete system (like a spin chain), with more complicated interactions between neighboring degrees of freedom (e.g., spins), like next-tonearest neighbors in addition to nearest neighbors
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
