Details
| Original language | English |
|---|---|
| Article number | 072903 |
| Number of pages | 14 |
| Journal | Journal of mathematical physics |
| Volume | 65 |
| Issue number | 7 |
| Early online date | 24 Jul 2024 |
| Publication status | Published - Jul 2024 |
Abstract
In 1977 Lüscher found a class of SO(4)-symmetric SU(2) Yang-Mills solutions in Minkowski space, which have been rederived 40 years later by employing the isometry S3 ≅ SU(2) and conformally mapping SU(2)-equivariant solutions of the Yang-Mills equations on (two copies of) de Sitter space d S 4 ≅ R × S 3 . Here we present the noncompact analog of this construction via AdS3 ≅ SU(1, 1). On (two copies of) anti-de Sitter space A d S 4 ≅ R × A d S 3 we write down SU(1,1)-equivariant Yang-Mills solutions and conformally map them to R 1 , 3 . This yields a two-parameter family of exact SU(1,1) Yang-Mills solutions on Minkowski space, whose field strengths are essentially rational functions of Cartesian coordinates. Gluing the two AdS copies happens on a dS3 hyperboloid in Minkowski space, and our Yang-Mills configurations are singular on a two-dimensional hyperboloid d S 3 ∩ R 1 , 2 . This renders their action and the energy infinite, although the field strengths fall off fast asymptotically except along the lightcone. We also construct Abelian solutions, which share these properties but are less symmetric and of zero action.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
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In: Journal of mathematical physics, Vol. 65, No. 7, 072903, 07.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Exact gauge fields from anti-de Sitter space
AU - Hirpara, Savan
AU - Kumar, Kaushlendra
AU - Lechtenfeld, Olaf
AU - Picanço Costa, Gabriel
N1 - Publisher Copyright: © 2024 Author(s).
PY - 2024/7
Y1 - 2024/7
N2 - In 1977 Lüscher found a class of SO(4)-symmetric SU(2) Yang-Mills solutions in Minkowski space, which have been rederived 40 years later by employing the isometry S3 ≅ SU(2) and conformally mapping SU(2)-equivariant solutions of the Yang-Mills equations on (two copies of) de Sitter space d S 4 ≅ R × S 3 . Here we present the noncompact analog of this construction via AdS3 ≅ SU(1, 1). On (two copies of) anti-de Sitter space A d S 4 ≅ R × A d S 3 we write down SU(1,1)-equivariant Yang-Mills solutions and conformally map them to R 1 , 3 . This yields a two-parameter family of exact SU(1,1) Yang-Mills solutions on Minkowski space, whose field strengths are essentially rational functions of Cartesian coordinates. Gluing the two AdS copies happens on a dS3 hyperboloid in Minkowski space, and our Yang-Mills configurations are singular on a two-dimensional hyperboloid d S 3 ∩ R 1 , 2 . This renders their action and the energy infinite, although the field strengths fall off fast asymptotically except along the lightcone. We also construct Abelian solutions, which share these properties but are less symmetric and of zero action.
AB - In 1977 Lüscher found a class of SO(4)-symmetric SU(2) Yang-Mills solutions in Minkowski space, which have been rederived 40 years later by employing the isometry S3 ≅ SU(2) and conformally mapping SU(2)-equivariant solutions of the Yang-Mills equations on (two copies of) de Sitter space d S 4 ≅ R × S 3 . Here we present the noncompact analog of this construction via AdS3 ≅ SU(1, 1). On (two copies of) anti-de Sitter space A d S 4 ≅ R × A d S 3 we write down SU(1,1)-equivariant Yang-Mills solutions and conformally map them to R 1 , 3 . This yields a two-parameter family of exact SU(1,1) Yang-Mills solutions on Minkowski space, whose field strengths are essentially rational functions of Cartesian coordinates. Gluing the two AdS copies happens on a dS3 hyperboloid in Minkowski space, and our Yang-Mills configurations are singular on a two-dimensional hyperboloid d S 3 ∩ R 1 , 2 . This renders their action and the energy infinite, although the field strengths fall off fast asymptotically except along the lightcone. We also construct Abelian solutions, which share these properties but are less symmetric and of zero action.
UR - http://www.scopus.com/inward/record.url?scp=85199567931&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2301.03606
DO - 10.48550/arXiv.2301.03606
M3 - Article
AN - SCOPUS:85199567931
VL - 65
JO - Journal of mathematical physics
JF - Journal of mathematical physics
SN - 0022-2488
IS - 7
M1 - 072903
ER -