# Lectures on Bulk Reconstruction

### Submission summary

 As Contributors: Nirmalya Kajuri Arxiv Link: https://arxiv.org/abs/2003.00587v7 (pdf) Date submitted: 2020-12-01 13:53 Submitted by: Kajuri, Nirmalya Submitted to: SciPost Physics Lecture Notes Academic field: Physics Specialties: Gravitation, Cosmology and Astroparticle Physics High-Energy Physics - Theory Approach: Theoretical

### Abstract

If the AdS/CFT conjecture holds, every question about bulk physics can be answered by the boundary CFT. But we still don't know how to translate all the questions about bulk physics to questions about the boundary CFT. Completing this bulk-boundary dictionary is the aim of the bulk reconstruction program, which we review in these lectures. We cover the HKLL construction, bulk reconstruction in AdS/Rindler, mirror operator construction of Papadodimas and Raju and the Marolf-Wall paradox. These notes are based on lectures given at ST4 2018.

###### Current status:
Has been resubmitted

I have corrected lingering typos and grammatical mistakes including the ones pointed out by the referee. To address the referee's comment we have added the following paragraph:

"For a CFT to have a semiclassical bulk dual, a set of conditions have to be fulfilled. We
refer the reader to [15, 16] for discussions on this issue. One key condition is that the CFT
should have a parameter N  1 which controls the factorization of the correlators of the
primary operators which are dual to bulk fields. This means if the two-point function of such
a primary operator is normalized to be of O(1), then higher correlators are suppressed as
hOiOjOki ∼ 1/Na
where a is some O(1) number. In particular, the correlators will follow Wick contraction for
infinite N. N is dual to the perturbative parameter in the bulk field theory, where a similar
factorization takes place in bulk correlators."

We hope this addresses the referee's question. The point is that if two-point functions in the CFT are normalized to order one, then higher order correlators are suppressed by powers of N. The corresponding object in the bulk dual theory is the coupling constant which plays an equivalent role in the factorization of bulk field correlators. We refer the referee to the discussion in section 2.4 of Daniel Harlow's TASI lectures. If this explanation is not satisfactory we can remove the action term from our notes.

### List of changes

1. We have corrected typos and grammatical mistakes that were present in the last manuscript, including the ones pointed out by the referee.

2. In response to the referee's first point, we have added to the first paragraph in page 5 which now reads:
"For a CFT to have a semiclassical bulk dual, a set of conditions have to be fulfilled. We
refer the reader to [15, 16] for discussions on this issue. One key condition is that the CFT
should have a parameter N  1 which controls the factorization of the correlators of the
primary operators which are dual to bulk fields. This means if the two-point function of such
a primary operator is normalized to be of O(1), then higher correlators are suppressed as
hOiOjOki ∼ 1/Na
where a is some O(1) number. In particular, the correlators will follow Wick contraction for
infinite N. N is dual to the perturbative parameter in the bulk field theory, where a similar
factorization takes place in bulk correlators."

### Submission & Refereeing History

Resubmission 2003.00587v8 on 15 January 2021

Resubmission 2003.00587v7 on 1 December 2020
Resubmission 2003.00587v4 on 14 July 2020
Submission 2003.00587v3 on 16 March 2020

## Reports on this Submission

### Anonymous Report 2 on 2021-1-14 Post-Editorial Recommendation Report (Invited Report)

• Cite as: Anonymous, Report on arXiv:2003.00587v7, delivered 2021-01-14, doi: 10.21468/SciPost.Report.2412

### Report

I concur with the first referee and am satisfied with the author's replies. In the refereeing process several conceptual points have been clarified and numerous typos have been corrected. I recommend proceeding with publication of the current version.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Anonymous Report 1 on 2021-1-4 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2003.00587v7, delivered 2021-01-04, doi: 10.21468/SciPost.Report.2361

### Report

This is my third round of refereeing of this manuscript (reflecting arXiv v7).
I am satisfied with the author's replies and I do not think it is necessary for me to pursue further questions. Two typos that were introduced on p.5 are as follows:

p.5 parag. 3: "Note that we have N is the only expansion parameter so far in the CFT." (Delete "we have").

p.5: $N$ is inconsistently italicized on this page and elsewhere.

At this point, I will leave further formatting issues to the editorial and typesetting teams' discretion.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -