SciPost Submission Page

Area law and OPE blocks in conformal field theory

by Jiang Long

Submission summary

As Contributors: Jiang Long
Preprint link: scipost_202010_00028v3
Date submitted: 2021-02-21 14:14
Submitted by: Long, Jiang
Submitted to: SciPost Physics Proceedings
Proceedings issue: 4th International Conference on Holography, String Theory and Discrete Approach in Hanoi
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.

Current status:
Editor-in-charge assigned


List of changes

1. Line 30-31 and 40, we added the discussion on OPE blocks , emphasising that OPE block provides a novel look at the modular Hamiltonian. This is also the motivation to relate OPE block to area law in this paper.
2. Line 35-37: we rewrote the UV divergences of the entanglement entropy.
3. Line 47-48: we wrote explicitly the possible values of the degree q. There is no fractional power of the logarithm.
4. Line 72: we added a sentence to extend the area law to general field theory.
5. Line 88-89: we discussed the possible logarithmic pieces with smaller power. They don't provide any universal information.
6. Line 94-97: we added one comment on the relation between the area law and OPE blocks.
7. Line 101: we changed "so(d-1) spin J_{ij} with magnitude J" to "so(d-1) spin J".
8. Line 120-121: we changed the "the external operators are the same" to "the external operators have the same quantum numbers".
9. Line 154-155: the constant c is related to normalization of the operator . This explains why we can set c=1.
10. Eq (2.26): \gamma\to\gamma(n).
11. Line 138: we added "(R=1)".
12.Line 196-198: we added the convergence problem of the summation of eq. (2.31).
13. Line 221-226: we discussed the coefficient D and conformal block G.
14. Line 317-319: the cyclic identity is a conjecture. We don't prove its validity, however, we can check it case by case.
15.Line 337-339: we added the discussion on the non-integer conformal weights.
16. Line 412: we changed "we restrict to the region m\ge 3" to "we consider type-(2) and type-(3) CCFs".
17. Line 414-415: we added the reference on the type-(4) CCF for free theory.
18. We rewrote (3.39) and (4.11).
19. We improved the writing of the paper.

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