Universal Bound on Effective Central Charge and Its Saturation
-
1.
The University of Texas System
-
2.
California Institute of Technology
-
3.
RIKEN
-
4.
Kyushu University
-
5.
University of Tokyo
Abstract
The effective central charge (denoted by c_(eff)) is a measure of entanglement through a conformal interface, while the transmission coefficient (encoded in the coefficient c_(LR) of the two-point function of the energy-momentum tensor across the interface) is a measure of energy transmission through the interface. It has been pointed out that these two are generally different. In this Letter, we propose the inequalities, 0≤c_(LR)≤c_(eff)≤min(c_L,c_R). They have the simple but important implication that the amount of energy transmission can never exceed the amount of information transmission. We verify them using the AdS/CFT correspondence, using the perturbation method, and in examples beyond holography. We also show that these inequalities are sharp by constructing a class of interfaces that saturate them.
Copyright and License
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Acknowledgement
We would like to thank Costas Bachas, Ilka Brunner, Shinsei Ryu, and Yifan Wang for careful reading and valuable comments on a draft of this Letter.
Funding
A. K., H. S., and M. W. are supported in part by the U.S. Department of Energy under Grant No. DE-SC0022021 and a grant from the Simons Foundation (Grant No. 651440, A. K.). H. O. and Y. K. are supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. In addition, Y. K. is supported by the Brinson Prize Fellowship at Caltech and the INAMORI Frontier Program at Kyushu University. H. O. is supported in part by the Simons Investigator Award (No. MP-SIP-00005259), the Guggenheim Fellowship, the World Premier International Research Center Initiative, MEXT, Japan, and JSPS Grants-in-Aid for Scientific Research 23K03379. This work was performed in part at the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1607611, and at the Kavli Institute for Theoretical Physics (KITP), which is supported by NSF Grant No. PHY-2309135.
Supplemental Material
The supplemental material presents a detail of the construction of an example on the CFT side that saturates the upper bound. This is just for readers who are interested in the explicit construction.
Files
| Name | Size | Download all |
|---|---|---|
|
md5:4dcca47fcbdc17ef79a8bc0bf36589b1
|
210.7 kB | Preview Download |
|
md5:b3c0a42e4119b3ee183f8553213caf2a
|
220.4 kB | Preview Download |
Additional details
- United States Department of Energy
- DE-SC0022021
- Simons Foundation
- 651440
- United States Department of Energy
- DE-SC0011632
- California Institute of Technology
- Kyushu University
- Simons Foundation
- Investigator Award MP-SIP-00005259
- Ministry of Education, Culture, Sports, Science and Technology
- Japan Society for the Promotion of Science
- 23K03379
- National Science Foundation
- PHY-1607611
- National Science Foundation
- PHY-2309135
- Accepted
-
2024-08-05Manuscript Accepted
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Publication Status
- Published