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Register a new userRelative entropy for coherent states in chiral CFT
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Stefan Hollands
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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.
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We show that the relative entropy between the reduced density matrix of the vacuum state in some region $A$ and that of an excited state created by a unitary operator localized at a small distance $ell$ of a boundary point $p$ is insensitive to the global shape of $A$, up to a small correction. This correction tends to zero as $ell/R$ tends to zero, where $R$ is a measure of the curvature of $partial A$ at $p$, but at a rate necessarily slower than $sim sqrt{ell/R}$ (in any dimension). Our arguments are mathematically rigorous and only use model-independent, basic assumptions about quantum field theory such as locality and Poincare invariance.
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