Publications at the Riemann Center
Exact gauge fields from anti-de Sitter space
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.
Details
- Organisation(s)
-
Institute of Theoretical Physics
Riemann Center for Geometry and Physics
- Type
- Article
- Journal
- Journal of mathematical physics
- Volume
- 65
- No. of pages
- 14
- ISSN
- 0022-2488
- Publication date
- 07.2024
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Statistical and Nonlinear Physics, Mathematical Physics
- Electronic version(s)
-
https://doi.org/10.1063/5.0150027 (Access:
Closed
)
https://doi.org/10.48550/arXiv.2301.03606 (Access: Open )
