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A low-energy limit of Yang-Mills theory on de Sitter space

2021    Cork, Josh; Kutluk, Emine; Lechtenfeld, Olaf; Popov, Alexander

We consider Yang-Mills theory with a compact structure group G on four-dimensional de Sitter space dS4. Using conformal invariance, we transform the theory from dS4 to the finite cylinder $I$ × S 3, where $I$ = (−π/2, π/2) and S 3 is the round three-sphere. By considering only bundles P → $I$ × S 3 which are framed over the temporal boundary ∂ $I$ × S 3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂ $I$ × S 3. We study the consequences of the framing on the variation of the action, and on the Yang-Mills equations. This allows for an infinite-dimensional moduli space of Yang-Mills vacua on dS4. We show that, in the low-energy limit, when momentum along $I$ is much smaller than along S 3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $M$ vac of gauge-inequivalent Yang-Mills vacua on S 3. Since $M$ vac ≅ C ∞(S 3, G)/G is a group manifold, the dynamics is expected to be integrable.