Relative entropy and the RG flow
Relative entropy and the RG flow
复制标题
相对熵和 RG 流
DOI：
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发表时间：
2016
期刊：
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通讯作者：
G. Torroba
中科院分区：
文献类型：
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作者：
H. Casini;Eduardo Testé;G. Torroba
本文考虑了两种不同理论真空态之间的相对熵：共形场论（CFT）和受相应算符扰动的CFT。通过将两个态限制在球的因果域中的零柯西曲面上，我们使得相对熵等于纠缠熵之差。因此，这种差异具有相对熵的正性和单调性。由此得出d = 2维时空中c定理的一个简单的替代证明，以及当d > 2时纠缠熵中面积项的系数沿着重整化群（RG）流在不动点之间减小的证明。我们评论的相对熵的收敛状态，取决于时空维度和共形维度Δ的扰动，触发RG流。
A bstractWe consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.