Domain Wall Equations, Hessian of Superpotential, and Bogomol'nyi Bounds
Dec 13, 201524 pages
Published in:
- Nucl.Phys.B 904 (2016) 470-493
- Published: Mar, 2016
e-Print:
- 1512.04080 [hep-th]
View in:
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Abstract: (arXiv)
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.Note:
- 25 pages
- domain wall
- superpotential
- BPS
- field theory
- field equations: solution
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