论文标题
在字段理论中对Beta功能的约束
Constraints on beta functions in field theories
论文作者
论文摘要
$β$ - 功能描述了在现场理论中的重新规范化组流下运行的耦合方式。通常，所有尊重对称性和局部性的耦合均在重新归一化的基团下产生，而确切的重新归一化组流的特征在于在耦合的无限尺寸空间中定义的$β$ - 功能。在本文中，我们表明，重新归一化组流量受到高度限制，因此在耦合的度量零子空间中定义的$β$ - 符合完全确定了整个耦合空间中的$β$ - 功能。我们提供了一种基于量子重新归一化的算法，用于从子空间中定义的$β$ - 功能中重建整个$β$ functions。作为示例，我们从单个跟踪耦合的子空间中定义的$ o_l（n）$ o_r（n）$矩阵模型得出了$ o（n）$ vector模型的完整$β$ functions和$ o_l（n）\ times o_r（n）$矩阵模型。
The $β$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact renormalization group flow is characterized by the $β$-functions defined in the infinite dimensional space of couplings. In this paper, we show that the renormalization group flow is highly constrained so that the $β$-functions defined in a measure zero subspace of couplings completely determine the $β$-functions in the entire space of couplings. We provide a quantum renormalization group-based algorithm for reconstructing the full $β$-functions from the $β$-functions defined in the subspace. As examples, we derive the full $β$-functions for the $O(N)$ vector model and the $O_L(N) \times O_R(N)$ matrix model entirely from the $β$-functions defined in the subspace of single-trace couplings.
