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

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 $$ \mathcal{I} $$ I × S3, where $$ \mathcal{I} $$ I = (−π/2, π/2) and S3 is the round three-sphere. By considering only bundles P → $$ \mathcal{I} $$ I × S3 which are framed over the temporal boundary ∂$$ \mathcal{I} $$ I × S3, we introduce additional degrees of freedom which restrict gauge transformations to be identity on ∂$$ \mathcal{I} $$ 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 $$ \mathcal{I} $$ I is much smaller than along S3, the Yang-Mills dynamics in dS4 is approximated by geodesic motion in the infinite-dimensional space $$ \mathcal{M} $$ M vac of gauge-inequivalent Yang-Mills vacua on S3. Since $$ \mathcal{M} $$ M vac ≅ C∞(S3, G)/G is a group manifold, the dynamics is expected to be integrable.