Perturbative expansions of Rényi relative divergences and holography
In this talk, I will introduce a novel way to perturbatively calculate Rényi relative divergences and related quantities without using replica trick as well as analytic continuation. I explicitly determine the form of the perturbative term at any order by an integral along the modular flow of the unperturbed state. By applying the prescription to a class of reduced density matrices in conformal field theory, I argue that the second order term of certain linear combination of the divergences has a holographic expression in terms of bulk symplectic form,
which is a one-parameter generalization of the statement "Fisher information = Bulk canonical energy”.