$c$ -跨维流中的函数
$c$-Functions in Flows Across Dimensions
摘要：
我们探讨了在不同时空维度的理论之间的重整化群流中的$c$ -函数的概念。我们一方面讨论UV和IR不动点理论中连接中心荷的函数，另一方面讨论沿流单调的函数。首先，利用跨维全息对偶RG流的几何性质和零能量条件的约束，构造了单调全息$c$ -函数，从而建立了跨维全息$c$ -定理.第二，我们使用纠缠熵的两种不同类型的纠缠区域的场论沿RG流跨维度构建候选$c$ -功能，满足两个标准之一，但不是两个。在适当的过程中，我们还讨论了一个有趣的连接角贡献的纠缠熵和拓扑结构的紧凑的内部空间。作为这两种方法的具体例子，我们全息研究扭曲紧化的4D $\mathcal N=4$ SYM和紧化的6D $\mathcal N=(2,0)$理论。
英文摘要：
We explore the notion of $c$-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic $c$-function and thereby establish a holographic $c$-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate $c$-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d $\mathcal N=4$ SYM and compactifications of 6d $\mathcal N=(2,0)$ theories.
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