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

Dec 13, 2015
24 pages
Published in:
  • Nucl.Phys.B 904 (2016) 470-493
  • Published: Mar, 2016
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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