揭示二维德西特空间中离散系列标量的共形对称性
Revealing the conformal symmetry of the discrete series scalars in dS${}_2$
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中文总结 AI 辅助
研究二维德西特空间中离散系列标量的共形对称性，利用标量场关于共形克利福德张量的等效描述找到共形对称变换，证明运动方程协变，还找到局部定义的无迹应力张量生成全局共形等距变换。
中文摘要 AI 辅助
在具有非零恒定里奇曲率的二维流形上，存在一个质量参数非零的标量场无限序列，其允许一对（反）全纯流。在德西特空间（$\mathrm{dS}_2$）中适当定义理论后，这些流的关联函数服从全局共形沃德恒等式。我们探讨这种全局共形对称性如何作为对标量场的作用体现。关键步骤是利用标量场关于共形克利福德张量的等效描述。由此，我们找到一个共形对称变换，它局部作用于共形克利福德张量，但非局部作用于标量场。我们表明运动方程相对于这些共形变换协变变换，并进一步在$\mathrm{dS}_2$和$\mathrm{AdS}_2$中找到一个无迹应力张量，它由共形克利福德张量局部定义，生成全局共形等距变换。
英文摘要
On two-dimensional manifolds with nonzero constant Ricci curvature, there exists an infinite sequence of scalar fields with nonzero mass parameter that admit a pair of (anti)-holomorphic currents. After suitably defining the theory in de Sitter space ($\mathrm{dS}_2$), correlation functions of these currents obey global conformal Ward identities. We address the question of how this global conformal symmetry manifests as an action on the scalar field. An essential step is in leveraging an equivalent description of the scalar field in terms of a conformal Killing tensor. Through this, we find a conformal symmetry transformation that acts locally on the conformal Killing tensor, but non-locally on the scalar field. We show that the equation of motion transforms covariantly with respect to these conformal transformations, and further find a traceless stress tensor in both $\mathrm{dS}_2$ and $\mathrm{AdS}_2$, locally defined in terms of the conformal Killing tensor, which generates the global conformal isometry transformations.
