Abstract
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 \( \mathcal{I} \) × S3, where \( \mathcal{I} \) = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → \( \mathcal{I} \) × S3 which are framed over the temporal boundary ∂\( \mathcal{I} \) × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂\( \mathcal{I} \) × S3. 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 \( \mathcal{I} \) is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space \( \mathcal{M} \)vac of gauge-inequivalent Yang-Mills vacua on S3. Since \( \mathcal{M} \)vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.
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Cork, J., Kutluk, E.Ş., Lechtenfeld, O. et al. A low-energy limit of Yang-Mills theory on de Sitter space. J. High Energ. Phys. 2021, 89 (2021). https://doi.org/10.1007/JHEP09(2021)089
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DOI: https://doi.org/10.1007/JHEP09(2021)089