Details
| Original language | English |
|---|---|
| Pages (from-to) | 139-148 |
| Number of pages | 10 |
| Journal | Letters in mathematical physics |
| Volume | 84 |
| Issue number | 2-3 |
| Early online date | 30 May 2008 |
| Publication status | Published - Jun 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.
Keywords
- Integrability, Non-Abelian vortices
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Letters in mathematical physics, Vol. 84, No. 2-3, 06.2008, p. 139-148.
Research output: Contribution to journal › Article › Research › 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 -