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

Abstract

We consider Yang--Mills theory with a compact structure group $G$ on four-dimensional de Sitter space dS${}_4$. Using conformal invariance, we transform the theory from dS${}_4$ to the finite cylinder $\mathcal{I}\times S^3$, where $\mathcal{I}=(-\pi /2,\pi /2)$ and $S^3$ is the round three-sphere. By considering only bundles $P\to \mathcal{I}\times S^3$ which are framed over the temporal boundary $\partial \mathcal{I}\times S^3$, we introduce additional degrees of freedom which restrict gauge transformations to be identity on $\partial \mathcal{I}\times S^3$. 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 dS${}_4$. We show that, in the low-energy limit, when momentum along $\mathcal{I}$ is much smaller than along $S^3$, the Yang--Mills dynamics in dS${}_4$ is approximated by geodesic motion in the infinite-dimensional space ${\mathcal{M}}_{\mathrm{vac}}$ of gauge-inequivalent Yang--Mills vacua on $S^3$. Since ${\mathcal{M}}_{\mathrm{vac}}\cong C^{\infty }(S^3,G)/G$ is a group manifold, the dynamics is expected to be integrable.

arXiv comment1+23 pages. v2: introduction extended, theory modifications clarified, references updated

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