Abstract
An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.
Highlights
Vortices, monopoles, and instantons are classical solutions of various equations of motion in quantum field theory describing particle-like behavior in interaction dynamics in one, two, three, and four spatial dimensions, respectively [50]
At the BPS coupling an important question arises: Are the original second-order equations of motion equivalent to their BPS-reduced first-order equations? In other words, are all finite-energy critical points of the field-theoretical energy functional the solutions of the BPS equations, and attain the BPS bounds? For the Abelian Higgs vortices, Taubes proved [28, 47] that the answer is yes, and for the non-Abelian Yang–Mills–Higgs monopoles, he established [48] that the answer is no such that there are nonminimal solutions of the Yang–Mills–Higgs equations in the BPS coupling which are not solutions to the BPS equations
In this paper we have carried out a systematic investigation on the puzzle for a general domain wall model governing a multiple real-component scalar field u = (u1, . . . , un) in terms of a superpotential so that the potential is given by
Summary
Vortices, monopoles, and instantons are classical solutions of various equations of motion in quantum field theory describing particle-like behavior in interaction dynamics in one, two, three, and four spatial dimensions, respectively [50]. In [24] Forgacs and Horvath presented a series of examples of field-theoretical models in one, two, and three spatial dimensions that allow non-contractible loops in their configuration spaces These models may be candidates for the occurrence of saddle-point solutions and host barriers to topological vacuum tunneling as in the electroweak theory [29, 32]. We state and prove our main theorem that the definiteness of the Hessian of the superpotential at at least one ground state (a phase domain) suffices to ensure that all finite-energy domain wall solutions are BPS.
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.
