Non-Abelian Vortices on Riemann Surfaces: an Integrable Case
| dc.creator | Popov, Alexander D. | |
| dc.date | 2008-01-05 | |
| dc.date | 2008-02-02 | |
| dc.date.accessioned | 2026-07-07T10:16:08Z | |
| dc.date.available | 2026-07-07T10:16:08Z | |
| dc.description | We 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.description | 8 pages; v2: typos fixed | |
| dc.identifier | https://arxiv.org/abs/0801.0808 | |
| dc.identifier | http://arxiv.org/abs/0801.0808 | |
| dc.identifier | Lett.Math.Phys.84:139-148,2008 | |
| dc.identifier | doi:10.1007/s11005-008-0243-x | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173400 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Non-Abelian Vortices on Riemann Surfaces: an Integrable Case | |
| dc.type | text |