Pure Yang–Mills Solutions on dS4

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  • Joint Institute for Nuclear Research (JINR)
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OriginalspracheEnglisch
Seiten (von - bis)854-859
Seitenumfang6
FachzeitschriftPhysics of particles and nuclei
Jahrgang49
Ausgabenummer5
PublikationsstatusVeröffentlicht - Sept. 2018

Abstract

Abstract: We consider pure SU(2) Yang–Mills theory on four-dimensional de Sitter space dS4 and construct smooth and spatially homogeneous classical Yang–Mills fields. Slicing dS4 as R×S3 via an SU(2)-equivariant ansatz we reduce the Yang–Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a particular three-dimensional potential. Its classical trajectories yield spatially homogeneous Yang–Mills solutions in a very simple explicit form, depending only on de Sitter time with an exponential decay in the past and future. These configurations have not only finite energy, but their action is also finite and bounded from below. We present explicit coordinate representations of the simplest examples (for the fundamental SU(2) representation). Instantons (Yang–Mills solutions on the Wick-rotated S4 and solutions on AdS4 are also briefly discussed.

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Pure Yang–Mills Solutions on dS4. / Ivanova, T. A.; Lechtenfeld, O.; Popov, A. D.
in: Physics of particles and nuclei, Jahrgang 49, Nr. 5, 09.2018, S. 854-859.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Ivanova TA, Lechtenfeld O, Popov AD. Pure Yang–Mills Solutions on dS4. Physics of particles and nuclei. 2018 Sep;49(5):854-859. doi: 10.1134/S1063779618050210, 10.15488/5355
Ivanova, T. A. ; Lechtenfeld, O. ; Popov, A. D. / Pure Yang–Mills Solutions on dS4. in: Physics of particles and nuclei. 2018 ; Jahrgang 49, Nr. 5. S. 854-859.
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N1 - Funding Information: ACKNOWLEDGMENTS This work was partially supported by the Deutsche Forschungsgemeinschaft under grant LE 838/13 and by the Heisenberg–Landau program. It is based upon work from COST Action MP1405 QSPACE, supported by COST (European Cooperation in Science and Technology).

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N2 - Abstract: We consider pure SU(2) Yang–Mills theory on four-dimensional de Sitter space dS4 and construct smooth and spatially homogeneous classical Yang–Mills fields. Slicing dS4 as R×S3 via an SU(2)-equivariant ansatz we reduce the Yang–Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a particular three-dimensional potential. Its classical trajectories yield spatially homogeneous Yang–Mills solutions in a very simple explicit form, depending only on de Sitter time with an exponential decay in the past and future. These configurations have not only finite energy, but their action is also finite and bounded from below. We present explicit coordinate representations of the simplest examples (for the fundamental SU(2) representation). Instantons (Yang–Mills solutions on the Wick-rotated S4 and solutions on AdS4 are also briefly discussed.

AB - Abstract: We consider pure SU(2) Yang–Mills theory on four-dimensional de Sitter space dS4 and construct smooth and spatially homogeneous classical Yang–Mills fields. Slicing dS4 as R×S3 via an SU(2)-equivariant ansatz we reduce the Yang–Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a particular three-dimensional potential. Its classical trajectories yield spatially homogeneous Yang–Mills solutions in a very simple explicit form, depending only on de Sitter time with an exponential decay in the past and future. These configurations have not only finite energy, but their action is also finite and bounded from below. We present explicit coordinate representations of the simplest examples (for the fundamental SU(2) representation). Instantons (Yang–Mills solutions on the Wick-rotated S4 and solutions on AdS4 are also briefly discussed.

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