  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.
