We consider the relative entropy between the vacuum state and a state obtained by applying an exponentiated stress tensor to the vacuum of a chiral conformal field theory on the lightray. The smearing function of the stress tensor can be viewed as a vector field on the real line generating a diffeomorphism. We show that the relative entropy is equal to c times the so-called Schwarzian action of the diffeomorphism. As an application of this result, we obtain a formula for the relative entropy between the vacuum and a solitonic state.

中文翻译：

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手性 CFT 中相干态的相对熵

我们考虑真空状态与通过将指数应力张量应用于光线手征共形场理论的真空而获得的状态之间的相对熵。应力张量的拖尾函数可以看作是实线上产生微分同胚的矢量场。我们证明相对熵等于微分同胚的所谓 Schwarzian 作用的 c 倍。作为该结果的应用，我们获得了真空和孤子态之间的相对熵的公式。