Details
| Original language | English |
|---|---|
| Article number | 125026 |
| Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |
| Volume | 77 |
| Issue number | 12 |
| Publication status | Published - 24 Jun 2008 |
Abstract
It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R3,1. I show that such solutions exist in SU(N) gauge theory on the spaces R2×S2 and R×S1×S2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T×S2, where T is R or S1. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the 4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R1,1×S2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R×S1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R×S1×S2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S1×S3 interpreted as chains of n instanton-anti-instanton pairs.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
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In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 77, No. 12, 125026, 24.06.2008.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Explicit non-Abelian monopoles and instantons in SU(N) pure Yang-Mills theory
AU - Popov, Alexander D.
PY - 2008/6/24
Y1 - 2008/6/24
N2 - It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R3,1. I show that such solutions exist in SU(N) gauge theory on the spaces R2×S2 and R×S1×S2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T×S2, where T is R or S1. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the 4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R1,1×S2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R×S1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R×S1×S2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S1×S3 interpreted as chains of n instanton-anti-instanton pairs.
AB - It is well known that there are no static non-Abelian monopole solutions in pure Yang-Mills theory on Minkowski space R3,1. I show that such solutions exist in SU(N) gauge theory on the spaces R2×S2 and R×S1×S2 with Minkowski signature (-+++). In the temporal gauge they are solutions of pure Yang-Mills theory on T×S2, where T is R or S1. Namely, imposing SO(3) invariance and some reality conditions, I consistently reduce the Yang-Mills model on the above spaces to a non-Abelian analog of the 4 kink model whose static solutions give SU(N) monopole (-antimonopole) configurations on the space R1,1×S2 via the above-mentioned correspondence. These solutions can also be considered as instanton configurations of Yang-Mills theory in 2+1 dimensions. The kink model on R×S1 admits also periodic sphaleron-type solutions describing chains of n kink-antikink pairs spaced around the circle S1 with arbitrary n>0. They correspond to chains of n static monopole-antimonopole pairs on the space R×S1×S2 which can also be interpreted as instanton configurations in 2+1 dimensional pure Yang-Mills theory at finite temperature (thermal time circle). I also describe similar solutions in Euclidean SU(N) gauge theory on S1×S3 interpreted as chains of n instanton-anti-instanton pairs.
UR - http://www.scopus.com/inward/record.url?scp=46149118633&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.77.125026
DO - 10.1103/PhysRevD.77.125026
M3 - Article
AN - SCOPUS:46149118633
VL - 77
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 12
M1 - 125026
ER -