# Area law and OPE blocks in conformal field theory

### Submission summary

 As Contributors: Jiang Long Preprint link: scipost_202010_00028v5 Date accepted: 2021-08-02 Date submitted: 2021-07-08 15:01 Submitted by: Long, Jiang Submitted to: SciPost Physics Proceedings Proceedings issue: Review of Particle Physics at PSI Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

This is an introduction to the relationship between area law and OPE blocks in conformal field theory.

Published as SciPost Phys. Proc. 4, 013 (2021)

### List of changes

1) The referee is still concerned with the normalization of Q, indeed it could change the value of p_q. In this paper, I already set it to be 1 in lines 152-153.

2) I soften my statement on the p_q in lines 335-336.

3) I changed cdots to \cdots in line 223 and identity to identities in line 337.

### Submission & Refereeing History

Resubmission scipost_202010_00028v5 on 8 July 2021
Resubmission scipost_202010_00028v4 on 21 May 2021
Resubmission scipost_202010_00028v3 on 21 February 2021
Resubmission scipost_202010_00028v2 on 30 December 2020
Submission scipost_202010_00028v1 on 30 October 2020

## Reports on this Submission

### Anonymous Report 1 on 2021-7-15 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202010_00028v5, delivered 2021-07-15, doi: 10.21468/SciPost.Report.3234

### Strengths

1- Proposes new observables in CFT.
2- Presents concrete computations and results.

### Weaknesses

1- It is unclear whether the key quantity $p_q$ is unambiguously defined for general operators.

### Report

The author studied nonlocal operators in CFT known as "OPE blocks" that generalize the modular Hamiltonian, computed their correlators and extracted the universal leading logarithmic piece in the small cutoff limit. The key results were a UV/IR relation (3.16) and a cyclic identity (3.29). The former was proven by exploiting conformal symmetry, and the latter was conjectured based on evidence. The author carried out concrete calculations with suitable regularization to obtain $p_q$ for operators of integer weights, and left open whether there is an unambiguous way to define $p_q$ for general operators.

I recommend the manuscript for publication.

• validity: high
• significance: good
• originality: high
• clarity: good
• formatting: perfect
• grammar: good