Details
| Original language | English |
|---|---|
| Pages (from-to) | 439-442 |
| Number of pages | 4 |
| Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |
| Volume | 748 |
| Early online date | 22 Jul 2015 |
| Publication status | Published - 2 Sept 2015 |
Abstract
We consider the Yang-Mills equations with a matrix gauge group G on the de Sitter dS4, anti-de Sitter AdS4 and Minkowski R3,1 spaces. On all these spaces one can introduce a doubly warped metric in the form ds2=-du2+f2dv2+h2dsH22, where f and h are the functions of u and dsH22 is the metric on the two-dimensional hyperbolic space H2. We show that in the adiabatic limit, when the metric on H2 is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS2, AdS2 or R1,1, respectively) into the based loop group ΩG=C∞(S1, G)/G of smooth maps from the boundary circle S1=∂H2 of H2 into the gauge group G. For compact groups G these harmonic map equations are reduced to equations of geodesics on ΩG, solutions of which yield magnetic-type configurations of Yang-Mills fields. The group ΩG naturally acts on their moduli space.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
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In: Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, Vol. 748, 02.09.2015, p. 439-442.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Loop groups in Yang-Mills theory
AU - Popov, Alexander D.
PY - 2015/9/2
Y1 - 2015/9/2
N2 - We consider the Yang-Mills equations with a matrix gauge group G on the de Sitter dS4, anti-de Sitter AdS4 and Minkowski R3,1 spaces. On all these spaces one can introduce a doubly warped metric in the form ds2=-du2+f2dv2+h2dsH22, where f and h are the functions of u and dsH22 is the metric on the two-dimensional hyperbolic space H2. We show that in the adiabatic limit, when the metric on H2 is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS2, AdS2 or R1,1, respectively) into the based loop group ΩG=C∞(S1, G)/G of smooth maps from the boundary circle S1=∂H2 of H2 into the gauge group G. For compact groups G these harmonic map equations are reduced to equations of geodesics on ΩG, solutions of which yield magnetic-type configurations of Yang-Mills fields. The group ΩG naturally acts on their moduli space.
AB - We consider the Yang-Mills equations with a matrix gauge group G on the de Sitter dS4, anti-de Sitter AdS4 and Minkowski R3,1 spaces. On all these spaces one can introduce a doubly warped metric in the form ds2=-du2+f2dv2+h2dsH22, where f and h are the functions of u and dsH22 is the metric on the two-dimensional hyperbolic space H2. We show that in the adiabatic limit, when the metric on H2 is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS2, AdS2 or R1,1, respectively) into the based loop group ΩG=C∞(S1, G)/G of smooth maps from the boundary circle S1=∂H2 of H2 into the gauge group G. For compact groups G these harmonic map equations are reduced to equations of geodesics on ΩG, solutions of which yield magnetic-type configurations of Yang-Mills fields. The group ΩG naturally acts on their moduli space.
UR - http://www.scopus.com/inward/record.url?scp=84938067788&partnerID=8YFLogxK
U2 - 10.1016/j.physletb.2015.07.041
DO - 10.1016/j.physletb.2015.07.041
M3 - Article
AN - SCOPUS:84938067788
VL - 748
SP - 439
EP - 442
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
SN - 0370-2693
ER -