Exact gauge fields from anti-de Sitter space

authored by

Savan Hirpara, Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço Costa

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.

Organisation(s)

Institute of Theoretical 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/10.48550/arXiv.2301.03606 (Access: Open)
https://doi.org/10.1063/5.0150027 (Access: Closed)