Bulk operator reconstruction and smearing techniques in AdS/CFT

Abstract

In this report, I will first examine the prescription which defines the bulk fields with boundary operators which is known as HKLL prescription. I will demonstrate when we consider free fileds in HKLL prescription, the commutator calculated using the three point function doesn’t commute at spacelike separation. By analyzing two- and three-point functions, I will show that the linear smearing transformation leads to non-local commutators in the bulk when interactions are considered. To address this non-locality, I will discuss a modification which introduces a bilocal correction term which provides a more efficient method computationally to reestablish spacelike commutativity. This bilocal correction is shown to cancel the unwanted non-local terms in the commutator, thus ensuring that the bulk operators satisfy commutativity at spacelike separation.