Non-Abelian Vortices on Riemann Surfaces: an Integrable Case

dc.creatorPopov, Alexander D.
dc.date2008-01-05
dc.date2008-02-02
dc.date.accessioned2026-07-07T10:16:08Z
dc.date.available2026-07-07T10:16:08Z
dc.descriptionWe consider U(n+1) Yang-Mills instantons on the space Σ\times S^2, where Σis a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n+1) instanton equations on Σ\times S^2 are equivalent to non-Abelian vortex equations on Σ. Solutions to these equations are given by pairs (A,ϕ), where A is a gauge potential of the group U(n) and ϕis a Higgs field in the fundamental representation of the group U(n). We briefly compare this model with other non-Abelian Higgs models considered recently. Afterwards we show that for g>1, when Σ\times S^2 becomes a gravitational instanton, the non-Abelian vortex equations are the compatibility conditions of two linear equations (Lax pair) and therefore the standard methods of integrable systems can be applied for constructing their solutions.
dc.description8 pages; v2: typos fixed
dc.identifierhttps://arxiv.org/abs/0801.0808
dc.identifierhttp://arxiv.org/abs/0801.0808
dc.identifierLett.Math.Phys.84:139-148,2008
dc.identifierdoi:10.1007/s11005-008-0243-x
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173400
dc.subjectHigh Energy Physics - Theory
dc.titleNon-Abelian Vortices on Riemann Surfaces: an Integrable Case
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