Possible non-perturbative corrections to bulk reconstruction

Abstract

It was shown by Kabat and Lifschytz that black holes with finite entropy have their correlation functions of semiclassical bulk operators close to the horizon deviate from their semi-classical values and are ill-defined inside the horizon. This, they argue is due to the behavior of the large-time behavior of the unitary CFT, and means that the region near and inside the horizon receives correction, to that end they propose a cut-o! on the boundary CFT as tcutoff which would regulate and ensure that the correlators are well behaved up to a certain point in time. This is done in an ad-hoc manner and it is this prescription that we want to highlight and give a more natural interpretation and manifestation to by using the wormhole metric. We think that the corrections required for finite N theories could be weaved into the geometry of space-time itself by using this metric, to that extent we hope to recover the results that are central to the ad-hoc time tcutoff that was put in place before by Kabat and Lifschytz. Thus in the thesis below we define and recover how the worm-hole metric imposes a natural cuto! in the boundary CFT which is symmetric, preserving the light-cone structure, we also derive the bulk to the boundary correlator and match their behavior with what Kabat and Lifschytz have in their work to validate the conjecture and propose the wormhole as an alternate to the tcutoff prescription. To achieve this, we re-derive all the results that they have had and thus learn of the procedure required to tackle such a problem. This will help us in the long run when we introduce the modified metric into the problem statement. By drawing parallels, we aim to provide a more natural explanation for the tmax cuto!—typically introduced ad hoc in these correlators—within the HKLL framework.