A perturbative expansion for entanglement entropy in string theory

We derive a perturbative expansion for space time entanglement entropy in string theory by comparing replica trick constructions on the target space and on the worldsheet. Requiring the two approaches to match implies a set of constrains on the amplitudes involved and produces a non-trivial relation among target space and world sheet entanglement. We will be mainly interested in bosonic string on a flat background but also discuss the superstring generalization.