arXiv 2104.020752021-04hep-thmath-phmath.MP

De Sitter空间上Yang-Mills理论的低能极限

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

Josh Cork, Emine Şeyma Kutluk, Olaf Lechtenfeld, Alexander D. Popov

备注：: 1+23 pages. v2: introduction extended, theory modifications clarified, references updated
发表信息：: J. High Energ. Phys. 2021, 89 (2021)
DOI：: 10.1007/JHEP09(2021)089

摘要：

考虑四维de Sitter空间dS $_4$上具有紧结构群$G$的杨-米尔斯理论.利用共形不变性，我们将dS $_4$理论转化为有限圆柱${\cal I}\times S^3$理论，其中${\cal I}=(-π/2, π/2)$和$S^3$是圆形三球面。通过只考虑在时间边界$\partial{\cal I}\times S^3$上形成的丛$P\to{\cal I}\times S^3$，我们引入了额外的自由度，限制了规范变换在$\partial{\cal I}\times S^3$上是恒等的。我们研究的后果框架上的变化的行动，和杨-米尔斯方程。这允许在dS $_4$上的杨-米尔斯真空的无限维模空间。我们证明，在低能极限下，当沿着${\cal I}$的动量远小于沿着$S^3$的动量时，dS $_4$中的杨-米尔斯动力学可以用$S^3$上规范不等效杨-米尔斯真空的无限维空间${\cal M}_{\rm vac}$中的测地线运动来近似。由于${\cal M}_{\rm vac}\cong C^\infty (S^3, G)/G$是一个群流形，动力学被期望是可积的。

英文摘要：

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 ${\cal I}=(-π/2, π/2)$ and $S^3$ is the round three-sphere. By considering only bundles $P\to{\cal I}\times S^3$ which are framed over the temporal 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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