# Relative entropy for coherent states in chiral CFT. (arXiv:1903.07508v2 [hep-th] UPDATED)

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.