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Register a new userA low-energy limit of Yang-Mills theory on de Sitter space
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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 ${cal I}times S^3$, where ${cal I}=(-pi/2, pi/2)$ and $S^3$ is the round three-sphere. By considering only bundles $Pto{cal I}times S^3$ which are framed over the boundary $partial{cal I}times S^3$, we introduce additional degrees of freedom which restrict gauge transformations to be identity on $partial{cal I}times S^3$. 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 ${cal I}$ is much smaller than along $S^3$, the Yang--Mills dynamics in dS$_4$ is approximated by geodesic motion in the infinite-dimensional space ${cal M}_{rm vac}$ of gauge-inequivalent Yang--Mills vacua on $S^3$. Since ${cal M}_{rm vac}cong C^infty (S^3, G)/G$ is a group manifold, the dynamics is expected to be integrable.
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