Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 139-148 |
| Seitenumfang | 10 |
| Fachzeitschrift | Letters in mathematical physics |
| Jahrgang | 84 |
| Ausgabenummer | 2-3 |
| Frühes Online-Datum | 30 Mai 2008 |
| Publikationsstatus | Veröffentlicht - Juni 2008 |
Abstract
We consider U(n + 1) Yang-Mills instantons on the space ∑ × S 2, where ∑ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on ∑ × S 2 are equivalent to non-Abelian vortex equations on ∑. Solutions to these equations are given by pairs (A,φ), where A is a gauge potential of the group U(n) and φ is 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 ∑ × 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.
ASJC Scopus Sachgebiete
- Physik und Astronomie (insg.)
- Statistische und nichtlineare Physik
- Mathematik (insg.)
- Mathematische Physik
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in: Letters in mathematical physics, Jahrgang 84, Nr. 2-3, 06.2008, S. 139-148.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Non-abelian vortices on riemann surfaces
T2 - An integrable case
AU - Popov, Alexander D.
PY - 2008/6
Y1 - 2008/6
N2 - We consider U(n + 1) Yang-Mills instantons on the space ∑ × S 2, where ∑ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on ∑ × S 2 are equivalent to non-Abelian vortex equations on ∑. Solutions to these equations are given by pairs (A,φ), where A is a gauge potential of the group U(n) and φ is 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 ∑ × 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.
AB - We consider U(n + 1) Yang-Mills instantons on the space ∑ × S 2, where ∑ is a compact Riemann surface of genus g. Using an SU(2)-equivariant dimensional reduction, we show that the U(n + 1) instanton equations on ∑ × S 2 are equivalent to non-Abelian vortex equations on ∑. Solutions to these equations are given by pairs (A,φ), where A is a gauge potential of the group U(n) and φ is 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 ∑ × 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.
KW - Integrability
KW - Non-Abelian vortices
UR - http://www.scopus.com/inward/record.url?scp=46649102830&partnerID=8YFLogxK
U2 - 10.1007/s11005-008-0243-x
DO - 10.1007/s11005-008-0243-x
M3 - Article
AN - SCOPUS:46649102830
VL - 84
SP - 139
EP - 148
JO - Letters in mathematical physics
JF - Letters in mathematical physics
SN - 0377-9017
IS - 2-3
ER -