Quadratic order constraints on gravity from Entanglement.

Abstract

Entanglement Entropy in the recent year has been a powerful tool to provide with new insights in various areas of Physics. One class of such attempts was to provide us insights about gravity in the context of gravity. Inspired by the approach taken by Ted Jacobson in deriving the Einstein's equations starting from Thermodynamical argument, We are exploring such a possibility starting from the Quantum informatic arguments. We take condition of positivity of relative entropy arising from the quantum mechanical arguments and imposing these arguments in the context of holography with the help of Ryu-Takayanagi formulation. Imposing these relative entropy conditions on the Quantum Field theories with Holographic dual, we impose constrains on the gravitational theories allowed in the holographic bulk. Following the approach developed by A. Sinha et al and A. Kaviraj et al, We systematically introduce Higher derivative perturbations in the Boundary eld theory to study the relative entropy and there by obtain constraints at non linear level for gravitational dual. We also compute the greens function required to compute the second order corrections to the Minimal surface area in the bulk homologous to the entangling region of boundary field theory. There by using the greens function we were able to compute the second order corrections to the relative entropy, Thus enabling impose constraints and check in the bulk gravitational theory is necessarily diffeomorphism Invariant.