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arXiv · 1512.04080

Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds

Shouxin Chen·Yisong Yang
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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.

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Shouxin Chen, Yisong Yang. 2015-12-13. Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds. https://doi.org/10.1016/j.nuclphysb.2016.01.021

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