Yang–Mills solutions on Minkowski space via non-compact coset spaces

authored by

Kaushlendra Kumar, Olaf Lechtenfeld, Gabriel Picanço Costa, Jona Röhrig

Abstract

We find a two-parameter family of solutions of the Yang–Mills equations for gauge group SO(1,3) on Minkowski space by foliating different parts of it with non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone is foliated with hyperbolic space H³≅SO(1,3)/SO(3), while the exterior of the lightcone employs de Sitter space dS≅3SO(1,3)/SO(1,2). The lightcone itself is parametrized by SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3) Yang–Mills system on the first two coset spaces yields a mechanical system with inverted double-well potential and the foliation parameter serving as an evolution parameter. Its known analytic solutions are periodic or runaway except for the kink. On the lightcone, only the vacuum solution remains. The constructed Yang–Mills field strength is singular across the lightcone and of infinite action due to the noncompact cosets. Its energy-momentum tensor takes a very simple form, with energy density of opposite signs inside and outside the lightcone.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

Type

Artikel

Journal

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volume

835

No. of pages

10

ISSN

0370-2693

Publication date

10.12.2022

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.48550/arXiv.2206.12009 (Access: Offen)
https://doi.org/10.1016/j.physletb.2022.137564 (Access: Offen)