Existence and Uniqueness of BPS Vacuum and Multi-vortices in Inhomogeneous Abelian Higgs Model

2024/09/21 by Jeon, SeungJun, Kim, Chanju, Kim, Yoonbai
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2409.14054

Abstract

The BPS limit of the inhomogeneous abelian Higgs model is considered in (1+2)-dimensions. The second order Bogomolny equation is examined in the presence of an inhomogeneity expressed as a function of spatial coordinates. Assuming a physically reasonable upper bound on the L²(ℝ²) norm of the inhomogeneity function, we prove the existence and the uniqueness of nontrivial BPS vacuum solution of zero energy and topological BPS multi-vortex solutions of quantized positive energies.

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