Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Bulk reconstruction and the Hartle-Hawking wavefunction

Daniel Louis Jafferis

TL;DR

Problem: whether bulk observables behind horizons admit a single linear mapping to exact CFT operators, given nonperturbative diffeomorphism constraints. Approach: use the Hartle-Hawking wavefunction in AdS to test nonperturbative invariance of bulk operators and construct gauge-fixed, boundary-relational observables. Findings: naive operators that seem to count topological features are not nonperturbatively gauge-invariant; however, appropriately gauge-fixed relational bulk operators yield a linear action on the full Hilbert space, consistent with AdS/CFT. Implications: supports a linear bulk-to-CFT map across the full EFT domain and provides a pathway to resolve the information paradox via nonperturbative diffeomorphism constraints and relational measurements.

Abstract

In this work, a relation is found between state dependence of bulk observables in the gauge/gravity correspondence and nonperturbative diffeomorphism invariance. Certain bulk constraints, such as the black hole information paradox, appear to obstruct the existence of a linear map from bulk operators to exact CFT operators that is valid over the entire expected range of validity of the bulk effective theory. By formulating the bulk gravitational physics in the Hartle-Hawking framework to address these nonperturbative IR questions, I will demonstrate, in the context of eternal AdS-Schwarzschild, that the problematic operators fail to satisfy the Hamiltonian constraints nonperturbatively. In this way, the map between bulk effective theory Hartle-Hawking wavefunctions and exact CFT states can be linear on the full Hilbert space.

Bulk reconstruction and the Hartle-Hawking wavefunction

TL;DR

Problem: whether bulk observables behind horizons admit a single linear mapping to exact CFT operators, given nonperturbative diffeomorphism constraints. Approach: use the Hartle-Hawking wavefunction in AdS to test nonperturbative invariance of bulk operators and construct gauge-fixed, boundary-relational observables. Findings: naive operators that seem to count topological features are not nonperturbatively gauge-invariant; however, appropriately gauge-fixed relational bulk operators yield a linear action on the full Hilbert space, consistent with AdS/CFT. Implications: supports a linear bulk-to-CFT map across the full EFT domain and provides a pathway to resolve the information paradox via nonperturbative diffeomorphism constraints and relational measurements.

Abstract

In this work, a relation is found between state dependence of bulk observables in the gauge/gravity correspondence and nonperturbative diffeomorphism invariance. Certain bulk constraints, such as the black hole information paradox, appear to obstruct the existence of a linear map from bulk operators to exact CFT operators that is valid over the entire expected range of validity of the bulk effective theory. By formulating the bulk gravitational physics in the Hartle-Hawking framework to address these nonperturbative IR questions, I will demonstrate, in the context of eternal AdS-Schwarzschild, that the problematic operators fail to satisfy the Hamiltonian constraints nonperturbatively. In this way, the map between bulk effective theory Hartle-Hawking wavefunctions and exact CFT states can be linear on the full Hilbert space.

Paper Structure

This paper contains 5 sections, 14 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Nonperturbative bulk reconstruction
  3. The Hartle-Hawking wavefunction in AdS
  4. Boundary relational operators
  5. Discussion

Figures (2)

  • Figure 1: The factorized vacuum state is produced by a pair of hemisphere asymptotic boundaries, while the black hole state is produced by an annulus asymptotic boundary. The metric is not the induced one associated to the figure. The left and right figures show the two gluings described in the text, with a disconnected versus a connected slice.
  • Figure 2: Here it is clear that these are simply two different bulk slices of the same configuration, described by the euclidean AdS saddle. The left shows the disconnected slice and the right shows the connected slice. The slices are at $t=0$. The black hole state is produced by the annulus asymptotic boundary in the middle of the spheres, while the vacuum is produced by the cap boundaries at the top and bottom of the spheres.