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Chaos bound in Bershadsky-Polyakov theory
Justin R. David,
Timothy J. Hollowood,
Surbhi Khetrapal,
Prem Kumar 
Journal of High Energy Physics, Volume: 2019, Issue: 10
Swansea University Author:
Prem Kumar
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DOI (Published version): 10.1007/jhep10(2019)077
Abstract
We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φ with large dimension∆ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be v...
| Published in: | Journal of High Energy Physics |
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| ISSN: | 1029-8479 |
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Springer Science and Business Media LLC
2019
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa52119 |
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<?xml version="1.0"?><rfc1807><datestamp>2019-10-17T09:57:37.2784844</datestamp><bib-version>v2</bib-version><id>52119</id><entry>2019-09-26</entry><title>Chaos bound in Bershadsky-Polyakov theory</title><swanseaauthors><author><sid>087fd097167d724ce1b13cb285741ef5</sid><ORCID>0000-0003-0867-4213</ORCID><firstname>Prem</firstname><surname>Kumar</surname><name>Prem Kumar</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2019-09-26</date><deptcode>SPH</deptcode><abstract>We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φ with large dimension∆ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaledeffective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when ∆ &#60; 0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with W_3^(2)symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension ∆ =−c/8. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent λ_L = 4π/β, violating the universal chaos bound.</abstract><type>Journal Article</type><journal>Journal of High Energy Physics</journal><volume>2019</volume><journalNumber>10</journalNumber><publisher>Springer Science and Business Media LLC</publisher><issnElectronic>1029-8479</issnElectronic><keywords/><publishedDay>7</publishedDay><publishedMonth>10</publishedMonth><publishedYear>2019</publishedYear><publishedDate>2019-10-07</publishedDate><doi>10.1007/jhep10(2019)077</doi><url>http://dx.doi.org/10.1007/jhep10(2019)077</url><notes/><college>COLLEGE NANME</college><department>Physics</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SPH</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2019-10-17T09:57:37.2784844</lastEdited><Created>2019-09-26T20:33:01.9460046</Created><authors><author><firstname>Justin R.</firstname><surname>David</surname><order>1</order></author><author><firstname>Timothy J.</firstname><surname>Hollowood</surname><order>2</order></author><author><firstname>Surbhi</firstname><surname>Khetrapal</surname><order>3</order></author><author><firstname>Prem</firstname><surname>Kumar</surname><orcid>0000-0003-0867-4213</orcid><order>4</order></author></authors><documents><document><filename>0052119-08102019093825.pdf</filename><originalFilename>JHEP10(2019)077.pdf</originalFilename><uploaded>2019-10-08T09:38:25.5100000</uploaded><type>Output</type><contentLength>1238113</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><embargoDate>2019-10-07T00:00:00.0000000</embargoDate><documentNotes>Released under the terms of a Creative Commons Attribution License (CC-BY).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
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2019-10-17T09:57:37.2784844 v2 52119 2019-09-26 Chaos bound in Bershadsky-Polyakov theory 087fd097167d724ce1b13cb285741ef5 0000-0003-0867-4213 Prem Kumar Prem Kumar true false 2019-09-26 SPH We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φ with large dimension∆ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaledeffective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when ∆ < 0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with W_3^(2)symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension ∆ =−c/8. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent λ_L = 4π/β, violating the universal chaos bound. Journal Article Journal of High Energy Physics 2019 10 Springer Science and Business Media LLC 1029-8479 7 10 2019 2019-10-07 10.1007/jhep10(2019)077 http://dx.doi.org/10.1007/jhep10(2019)077 COLLEGE NANME Physics COLLEGE CODE SPH Swansea University 2019-10-17T09:57:37.2784844 2019-09-26T20:33:01.9460046 Justin R. David 1 Timothy J. Hollowood 2 Surbhi Khetrapal 3 Prem Kumar 0000-0003-0867-4213 4 0052119-08102019093825.pdf JHEP10(2019)077.pdf 2019-10-08T09:38:25.5100000 Output 1238113 application/pdf Version of Record true 2019-10-07T00:00:00.0000000 Released under the terms of a Creative Commons Attribution License (CC-BY). true eng https://creativecommons.org/licenses/by/4.0/ |
| title |
Chaos bound in Bershadsky-Polyakov theory |
| spellingShingle |
Chaos bound in Bershadsky-Polyakov theory Prem Kumar |
| title_short |
Chaos bound in Bershadsky-Polyakov theory |
| title_full |
Chaos bound in Bershadsky-Polyakov theory |
| title_fullStr |
Chaos bound in Bershadsky-Polyakov theory |
| title_full_unstemmed |
Chaos bound in Bershadsky-Polyakov theory |
| title_sort |
Chaos bound in Bershadsky-Polyakov theory |
| author_id_str_mv |
087fd097167d724ce1b13cb285741ef5 |
| author_id_fullname_str_mv |
087fd097167d724ce1b13cb285741ef5_***_Prem Kumar |
| author |
Prem Kumar |
| author2 |
Justin R. David Timothy J. Hollowood Surbhi Khetrapal Prem Kumar |
| format |
Journal article |
| container_title |
Journal of High Energy Physics |
| container_volume |
2019 |
| container_issue |
10 |
| publishDate |
2019 |
| institution |
Swansea University |
| issn |
1029-8479 |
| doi_str_mv |
10.1007/jhep10(2019)077 |
| publisher |
Springer Science and Business Media LLC |
| url |
http://dx.doi.org/10.1007/jhep10(2019)077 |
| document_store_str |
1 |
| active_str |
0 |
| description |
We consider two dimensional conformal field theory (CFT) with large central charge c in an excited state obtained by the insertion of an operator Φ with large dimension∆ ∼ O(c) at spatial infinities in the thermal state. We argue that correlation functions of light operators in such a state can be viewed as thermal correlators with a rescaledeffective temperature. The effective temperature controls the growth of out-of-time order (OTO) correlators and results in a violation of the universal upper bound on the associated Lyapunov exponent when ∆ < 0 and the CFT is nonunitary. We present a specific realization of this situation in the holographic Chern-Simons formulation of a CFT with W_3^(2)symmetry also known as the Bershadsky-Polyakov algebra. We examine the precise correspondence between the semiclassical (large-c) representations of this algebra and the Chern-Simons formulation, and infer that the holographic CFT possesses a discretuum of degenerate ground states with negative conformal dimension ∆ =−c/8. Using the Wilson line prescription to compute entanglement entropy and OTO correlators in the holographic CFT undergoing a local quench, we find the Lyapunov exponent λ_L = 4π/β, violating the universal chaos bound. |
| published_date |
2019-10-07T04:04:19Z |
| _version_ |
1763753338500808704 |
| score |
11.013731 |