Details
| Original language | English |
|---|---|
| Article number | 061601 |
| Journal | Physical review letters |
| Volume | 119 |
| Issue number | 6 |
| Publication status | Published - 11 Aug 2017 |
Abstract
We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. 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 double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τR is given by Ba=-12Ia/(R2cosh2τ), where Ia for a=1, 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -12j(j+1)(2j+1)π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- General Physics and Astronomy
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In: Physical review letters, Vol. 119, No. 6, 061601, 11.08.2017.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space
AU - Ivanova, Tatiana A.
AU - Lechtenfeld, Olaf
AU - Popov, Alexander D.
N1 - Publisher Copyright: © 2017 American Physical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/8/11
Y1 - 2017/8/11
N2 - We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. 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 double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τR is given by Ba=-12Ia/(R2cosh2τ), where Ia for a=1, 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -12j(j+1)(2j+1)π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.
AB - We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. 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 double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τR is given by Ba=-12Ia/(R2cosh2τ), where Ia for a=1, 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -12j(j+1)(2j+1)π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.
UR - http://www.scopus.com/inward/record.url?scp=85027834487&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.119.061601
DO - 10.1103/PhysRevLett.119.061601
M3 - Article
C2 - 28949611
AN - SCOPUS:85027834487
VL - 119
JO - Physical review letters
JF - Physical review letters
SN - 0031-9007
IS - 6
M1 - 061601
ER -