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:  20210221 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: 

Approach:  Theoretical 
Abstract
This is an introduction to the relationship between area law and OPE blocks in conformal field theory.
Current status:
List of changes
1. Line 3031 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 3537: we rewrote the UV divergences of the entanglement entropy.
3. Line 4748: 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 8889: we discussed the possible logarithmic pieces with smaller power. They don't provide any universal information.
6. Line 9497: we added one comment on the relation between the area law and OPE blocks.
7. Line 101: we changed "so(d1) spin J_{ij} with magnitude J" to "so(d1) spin J".
8. Line 120121: we changed the "the external operators are the same" to "the external operators have the same quantum numbers".
9. Line 154155: 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 196198: we added the convergence problem of the summation of eq. (2.31).
13. Line 221226: we discussed the coefficient D and conformal block G.
14. Line 317319: the cyclic identity is a conjecture. We don't prove its validity, however, we can check it case by case.
15.Line 337339: we added the discussion on the noninteger 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 414415: 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.