From sources to initial data and back again: on bulk singularities in Euclidean AdS/CFT

TL;DR

This paper investigates how Euclidean path integrals with sources in AdS/CFT can generate initial data, revealing that only analytic initial data without singularities can be prepared, and singularities are interpreted as non-perturbative effects.

Contribution

It characterizes the class of initial data obtainable via Euclidean sources in AdS/CFT and interprets bulk singularities as non-perturbative phenomena.

Findings

Initial data must be analytic to be prepared by Euclidean sources.

Bulk regularity constrains the subset of initial data.

Singularities in Euclidean sections are linked to non-perturbative objects.

Abstract

A common method to prepare states in AdS/CFT is to perform the Euclidean path integral with sources turned on for single-trace operators. These states can be interpreted as coherent states of the bulk quantum theory associated to Lorentzian initial data on a Cauchy slice. In this paper, we discuss the extent to which arbitrary initial data can be obtained in this way. We show that the initial data must be analytic and define the subset of it that can be prepared by imposing bulk regularity. Turning this around, we show that for generic analytic initial data the corresponding Euclidean section contains singularities coming from delta function sources in the bulk. We propose an interpretation of these singularities as non-perturbative objects in the microscopic theory.