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

DOI10.1007/JHEP09(2021)089zbMATH Open1472.70054arXiv2104.02075MaRDI QIDQ2237626

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Publication date: 27 October 2021

Published in: (Search for Journal in Brave)

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 $calIimes{S}^3$, where $calI=(-pi/2,pi/2)$ and $S^3$ is the round three-sphere. By considering only bundles $PocalIimes{S}^3$ which are framed over the temporal boundary $partialcalIimes{S}^3$, we introduce additional degrees of freedom which restrict gauge transformations to be identity on $partialcalIimes{S}^3$. 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 $calI$ is much smaller than along $S^3$, the Yang--Mills dynamics in dS${}_4$ is approximated by geodesic motion in the infinite-dimensional space ${calM}_{mvac}$ of gauge-inequivalent Yang--Mills vacua on $S^3$. Since ${calM}_{mvac}cong{C}^{i}nfty(S^3,G)/G$ is a group manifold, the dynamics is expected to be integrable.

Full work available at URL: https://arxiv.org/abs/2104.02075

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