Towards a C-theorem in defect CFT
Towards a C-theorem in defect CFT
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DOI：
10.1007/jhep01(2019)039
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发表时间：
2018-10
影响因子：
5.4
通讯作者：
Nozomu Kobayashi;T. Nishioka;Y. Sato;Kento Watanabe
中科院分区：
文献类型：
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作者：
Nozomu Kobayashi;T. Nishioka;Y. Sato;Kento Watanabe
我们探索缺陷共形场论 (DCFT) 中的 C 定理，它统一了迄今为止所有已知的猜想和定理。我们在包括全息模型在内的许多示例中检查了作为候选 C 函数的共形缺陷对球体自由能和整个球体的纠缠熵的额外贡献。我们发现，当适当正则化时，对于余维一缺陷（或边界），这两个量是等价的，但在其他方面则因通用常数项而不同。此外，我们在一些场论例子中发现，球体自由能降低，但纠缠熵沿着由缺陷局域扰动触发的特定重正化群（RG）流增加，假设具有无缺陷的平凡红外不动点。因此，我们在 DCFT 中提出了一个 C 定理，指出由于缺陷而导致的正则化球自由能的增量在任何缺陷 RG 流下都不会增加。我们还在缺陷 RG 流的几个全息模型中提供了我们建议的证明。
We explore a C-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate C-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a C-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.