Flood, SP and Speight, JM orcid.org/0000-0002-6844-9539 (2018) Chern–Simons deformation of vortices on compact domains. Journal of Geometry and Physics, 133. pp. 153-167. ISSN 0393-0440
Abstract
Existence of Maxwell-Chern–Simons-Higgs (MCSH) vortices in a Hermitian line bundle Ł over a general compact Riemann surface Σ is proved by a continuation method. The solutions are proved to be smooth both spatially and as functions of the Chern–Simons deformation parameter κ, and exist for all |κ|< κ∗, where κ∗ depends, in principle, on the geometry of Σ, the degree n of Ł, which may be interpreted as the vortex number, and the vortex positions. A simple upper bound on κ∗, depending only on n andthe volume of Σ, is found. Further, it is proved that a positive lower bound on κ∗, depending on Σ and n, but independent of vortex positions, exists. A detailed numerical study of rotationally equivariant vortices on round two-spheres is performed. We find that κ∗ in general does depend on vortex positions, and, for fixed n andradius, tends to be larger the more evenly vortices are distributed between the North and South poles. A generalization of the MCSH model to compact Kähler domains Σ of complex dimension k≥1 is formulated. The Chern–Simons term is replaced by the integral over spacetime of A∧F∧ωk⁻¹, where ω is the Kähler form on Σ. A topological lower bound on energy is found, attained by solutions of a deformed version of the usual vortex equations on Σ. Existence, uniqueness and smoothness of vortex solutions of these generalized equations is proved, for |κ|< κ∗, and an upper bound on κ∗ depending only on the Kähler class of Σ andthe first Chern class of Ł is obtained.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier B.V. This is an author produced version of a paper published in Journal of Geometry and Physics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Vortices; Gauge theory; Chern–Simons theory; Topological solitons |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 11 Jul 2018 13:27 |
Last Modified: | 21 Jul 2019 00:42 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.geomphys.2018.07.009 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:133191 |