Rényi entropy, stationarity, and entanglement of the conformal scalar
We extend previous work on the perturbative expansion of the Rényi entropy, Sq , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2017
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| Online Access: | http://hdl.handle.net/1721.1/106642 https://orcid.org/0000-0001-9531-1319 |
| _version_ | 1826212551150534656 |
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| author | Lee, Jeongseog Lewkowycz, Aitor Perlmutter, Eric Safdi, Benjamin Ryan |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Lee, Jeongseog Lewkowycz, Aitor Perlmutter, Eric Safdi, Benjamin Ryan |
| author_sort | Lee, Jeongseog |
| collection | MIT |
| description | We extend previous work on the perturbative expansion of the Rényi entropy, Sq , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of N=4 super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass. |
| first_indexed | 2024-09-23T15:24:57Z |
| format | Article |
| id | mit-1721.1/106642 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:24:57Z |
| publishDate | 2017 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1066422022-09-29T14:39:00Z Rényi entropy, stationarity, and entanglement of the conformal scalar Lee, Jeongseog Lewkowycz, Aitor Perlmutter, Eric Safdi, Benjamin Ryan Massachusetts Institute of Technology. Department of Physics Safdi, Benjamin Ryan We extend previous work on the perturbative expansion of the Rényi entropy, Sq , around q = 1 for a spherical entangling surface in a general CFT. Applied to conformal scalar fields in various spacetime dimensions, the results appear to conflict with the known conformal scalar Rényi entropies. On the other hand, the perturbative results agree with known Rényi entropies in a variety of other theories, including theories of free fermions and vector fields and theories with Einstein gravity duals. We propose a resolution stemming from a careful consideration of boundary conditions near the entangling surface. This is equivalent to a proper treatment of total-derivative terms in the definition of the modular Hamiltonian. As a corollary, we are able to resolve an outstanding puzzle in the literature regarding the Rényi entropy of N=4 super-Yang-Mills near q = 1. A related puzzle regards the question of stationarity of the renormalized entanglement entropy (REE) across a circle for a (2+1)-dimensional massive scalar field. We point out that the boundary contributions to the modular Hamiltonian shed light on the previously-observed non-stationarity. Moreover, IR divergences appear in perturbation theory about the massless fixed point that inhibit our ability to reliably calculate the REE at small non-zero mass. National Science Foundation (U.S.) (grant PHY-1314198) 2017-01-26T22:04:38Z 2017-01-26T22:04:38Z 2015-03 2016-05-23T09:37:05Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 http://hdl.handle.net/1721.1/106642 Lee, Jeongseog et al. “Rényi Entropy, Stationarity, and Entanglement of the Conformal Scalar.” Journal of High Energy Physics 2015.3 (2015): n. pag. https://orcid.org/0000-0001-9531-1319 en http://dx.doi.org/10.1007/JHEP03(2015)075 Journal of High Energy Physics Creative Commons Attribution http://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Lee, Jeongseog Lewkowycz, Aitor Perlmutter, Eric Safdi, Benjamin Ryan Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title | Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title_full | Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title_fullStr | Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title_full_unstemmed | Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title_short | Rényi entropy, stationarity, and entanglement of the conformal scalar |
| title_sort | renyi entropy stationarity and entanglement of the conformal scalar |
| url | http://hdl.handle.net/1721.1/106642 https://orcid.org/0000-0001-9531-1319 |
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