Zero-energy states in conformal field theory with sine-square deformation
We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $\left| {0} \right\rangle$. We then introduce...
Saved in:
| Published in | Progress of theoretical and experimental physics Vol. 2017; no. 11 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Oxford University Press
01.11.2017
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2050-3911 2050-3911 |
| DOI | 10.1093/ptep/ptx147 |
Cover
| Abstract | We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $\left| {0} \right\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Möbius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable. |
|---|---|
| AbstractList | We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $\left| {0} \right\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Möbius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable. |
| Author | Tamura, Shota Katsura, Hosho |
| Author_xml | – sequence: 1 givenname: Shota surname: Tamura fullname: Tamura, Shota email: tamura@cams.phys.s.u-tokyo.ac.jp organization: Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan – sequence: 2 givenname: Hosho surname: Katsura fullname: Katsura, Hosho organization: Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan |
| BookMark | eNp9kM1LAzEQxYNUsNae_AcCghdZnTTZr6MUv6DgRS9eQpqdtSnbZJtk0f73brseRNDLzBx-7w3vnZKRdRYJOWdwzaDkN23Eth-fTORHZDyDFBJeMjb6cZ-QaQhrAGCQ5yDYmDy9oXcJWvTvOxqiihiosVQ7Wzu_UQ2tDTYVjSt0fkc_TFzRYCwmYdspj7TCAxaNs2fkuFZNwOn3npDX-7uX-WOyeH54mt8uEs0LEZM8FyVmOQJDLZaFYjotsrISFQctNAcmUsUZ1sirWYG8FGwJszorCwVLASnyCbkYfFvvth2GKNeu87Z_KTnL-_BZmkJPXQ2U9i4Ej7Vsvdkov5MM5L4uua9LDnX1NPtFaxMPqaJXpvlDczloXNf-a_4F9_t_MQ |
| CitedBy_id | crossref_primary_10_1103_PhysRevX_10_031036 crossref_primary_10_1103_PhysRevResearch_2_023085 crossref_primary_10_1103_PhysRevResearch_3_023044 crossref_primary_10_1103_PhysRevE_104_034133 crossref_primary_10_21468_SciPostPhys_10_2_049 crossref_primary_10_7566_JPSJ_94_031004 crossref_primary_10_1103_PhysRevResearch_6_023001 crossref_primary_10_1103_PhysRevB_102_205125 crossref_primary_10_1103_PhysRevB_109_054301 crossref_primary_10_1103_PhysRevB_97_184309 crossref_primary_10_1088_1751_8121_ab8c63 crossref_primary_10_1088_1751_8121_ab3944 crossref_primary_10_1093_ptep_pty058 crossref_primary_10_1103_PhysRevD_103_056005 crossref_primary_10_1093_ptep_ptaa077 crossref_primary_10_1103_PhysRevD_109_126014 crossref_primary_10_21468_SciPostPhys_13_4_082 crossref_primary_10_1007_JHEP09_2023_087 crossref_primary_10_1103_PhysRevB_98_140405 crossref_primary_10_7566_JPSJ_91_034001 |
| Cites_doi | 10.1103/PhysRevB.87.115128 10.7566/JPSJ.84.094706 10.1143/PTP.123.393 10.1088/1751-8113/48/44/445208 10.1103/PhysRevB.84.165132 10.1143/PTP.122.953 10.1093/ptep/ptw060 10.1088/1751-8113/44/25/252001 10.1103/PhysRevB.83.060414 10.1088/1751-8113/45/11/115003 10.1103/PhysRevA.83.052118 10.1103/PhysRevB.93.235119 10.1142/S0217751X16501700 10.1103/PhysRevB.84.115116 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. 2017 The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. 2017 – notice: The Author(s) 2017. Published by Oxford University Press on behalf of the Physical Society of Japan. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | TOX AAYXX CITATION 3V. 7XB 88I 8FK ABUWG AFKRA AZQEC BENPR CCPQU DWQXO GNUQQ HCIFZ M2P PHGZM PHGZT PIMPY PKEHL PQEST PQQKQ PQUKI PRINS Q9U |
| DOI | 10.1093/ptep/ptx147 |
| DatabaseName | Oxford Journals Open Access Collection CrossRef ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Central ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection Science Database Proquest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China ProQuest Central Basic |
| DatabaseTitle | CrossRef Publicly Available Content Database ProQuest Science Journals (Alumni Edition) ProQuest Central Student ProQuest One Academic Middle East (New) ProQuest Central Basic ProQuest Central Essentials ProQuest Science Journals ProQuest One Academic Eastern Edition ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Academic UKI Edition ProQuest Central Korea ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) ProQuest Central (Alumni) |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: TOX name: Oxford Journals Open Access Collection url: https://academic.oup.com/journals/ sourceTypes: Publisher – sequence: 2 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 2050-3911 |
| ExternalDocumentID | 10_1093_ptep_ptx147 10.1093/ptep/ptx147 |
| GroupedDBID | .I3 0R~ 4.4 5VS AAFWJ AAMVS AAPPN AAPXW AAVAP ABEJV ABGNP ABPTD ABXVV ACGFS ADHZD AENEX AENZO AFPKN AFULF AIBLX ALMA_UNASSIGNED_HOLDINGS ALUQC AMNDL BAYMD BTTYL CIDKT D~K EBS EJD ER. GROUPED_DOAJ H13 IAO ISR ITC KQ8 KSI M~E O9- OAWHX OJQWA OK1 PEELM RHF ROL ROX RXO TOX ~D7 88I AAYXX ABUWG AFKRA AZQEC BENPR CCPQU CITATION DWQXO GNUQQ HCIFZ M2P PHGZM PHGZT PIMPY 3V. 7XB 8FK PKEHL PQEST PQQKQ PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c384t-7749e67e01ec4b8a1c5869d4d30c4c30145a31efe3d28e3941b02f698a0b405e3 |
| IEDL.DBID | BENPR |
| ISSN | 2050-3911 |
| IngestDate | Mon Jun 30 12:23:12 EDT 2025 Thu Apr 24 23:12:51 EDT 2025 Tue Jul 01 02:09:13 EDT 2025 Fri Jan 31 08:06:30 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 11 |
| Keywords | A10 A46 B34 A63 |
| Language | English |
| License | This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c384t-7749e67e01ec4b8a1c5869d4d30c4c30145a31efe3d28e3941b02f698a0b405e3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://www.proquest.com/docview/3171476550?pq-origsite=%requestingapplication% |
| PQID | 3171476550 |
| PQPubID | 7121340 |
| ParticipantIDs | proquest_journals_3171476550 crossref_primary_10_1093_ptep_ptx147 crossref_citationtrail_10_1093_ptep_ptx147 oup_primary_10_1093_ptep_ptx147 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2017-11-01 |
| PublicationDateYYYYMMDD | 2017-11-01 |
| PublicationDate_xml | – month: 11 year: 2017 text: 2017-11-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Oxford |
| PublicationPlace_xml | – name: Oxford |
| PublicationTitle | Progress of theoretical and experimental physics |
| PublicationYear | 2017 |
| Publisher | Oxford University Press |
| Publisher_xml | – name: Oxford University Press |
| References | ( key 20171129104806_B6) 2012; 86 ( key 20171129104806_B16) 2016; 2016 ( key 20171129104806_B1) 2009; 122 ( key 20171129104806_B7) 2013; 87 ( key 20171129104806_B10) 2011; 84 ( key 20171129104806_B12) 2012; 45 ( key 20171129104806_B14) 1998 ( key 20171129104806_B2) 2010; 123 ( key 20171129104806_B5) 2011; 84 ( key 20171129104806_B8) 2015; 84 ( key 20171129104806_B19) (2015); 05 ( key 20171129104806_B13) 1997 ( key 20171129104806_B3) 2011; 83 ( key 20171129104806_B15) 2016; 31 ( key 20171129104806_B11) 2015; 48 ( key 20171129104806_B18) 2015; 30 ( key 20171129104806_B4) 2011; 83 ( key 20171129104806_B17) 2016; 93 ( key 20171129104806_B9) 2011; 44 |
| References_xml | – volume: 30 start-page: 1550092 year: 2015 ident: key 20171129104806_B18 publication-title: Mod. Phys. Lett. A – volume: 05 start-page: 113 year: (2015) ident: key 20171129104806_B19 publication-title: J. High Energy Phys. – volume: 87 start-page: 115128 year: 2013 ident: key 20171129104806_B7 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.87.115128 – volume: 84 start-page: 094706 year: 2015 ident: key 20171129104806_B8 publication-title: J. Phys. Soc. Jpn. doi: 10.7566/JPSJ.84.094706 – volume: 123 start-page: 393 year: 2010 ident: key 20171129104806_B2 publication-title: Prog. Theor. Phys. doi: 10.1143/PTP.123.393 – volume: 48 start-page: 445208 year: 2015 ident: key 20171129104806_B11 publication-title: J. Phys. A: Math. Theor. doi: 10.1088/1751-8113/48/44/445208 – volume: 84 start-page: 165132 year: 2011 ident: key 20171129104806_B10 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.84.165132 – volume: 122 start-page: 953 year: 2009 ident: key 20171129104806_B1 publication-title: Prog. Theor. Phys. doi: 10.1143/PTP.122.953 – volume: 2016 start-page: 063A02 year: 2016 ident: key 20171129104806_B16 publication-title: Prog. Theor. Exp. Phys. doi: 10.1093/ptep/ptw060 – volume-title: Conformal Field Theory year: 1997 ident: key 20171129104806_B13 – volume: 44 start-page: 252001 year: 2011 ident: key 20171129104806_B9 publication-title: J. Phys. A: Math. Theor. doi: 10.1088/1751-8113/44/25/252001 – volume: 83 start-page: 060414(R) year: 2011 ident: key 20171129104806_B3 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.83.060414 – volume: 45 start-page: 115003 year: 2012 ident: key 20171129104806_B12 publication-title: J. Phys. A: Math. Theor. doi: 10.1088/1751-8113/45/11/115003 – volume-title: Conformal Invariance and Critical Phenomena year: 1998 ident: key 20171129104806_B14 – volume: 83 start-page: 052118 year: 2011 ident: key 20171129104806_B4 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.83.052118 – volume: 86 start-page: 041108(R) year: 2012 ident: key 20171129104806_B6 publication-title: Phys. Rev. B – volume: 93 start-page: 235119 year: 2016 ident: key 20171129104806_B17 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.93.235119 – volume: 31 start-page: 1650170 year: 2016 ident: key 20171129104806_B15 publication-title: Int. J. Mod. Phys. A doi: 10.1142/S0217751X16501700 – volume: 84 start-page: 115116 year: 2011 ident: key 20171129104806_B5 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.84.115116 |
| SSID | ssj0001077041 |
| Score | 2.239203 |
| Snippet | We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the... |
| SourceID | proquest crossref oup |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| SubjectTerms | Boundary conditions Coordinate transformations Eigenvalues Energy Norms |
| Title | Zero-energy states in conformal field theory with sine-square deformation |
| URI | https://www.proquest.com/docview/3171476550 |
| Volume | 2017 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3PS8MwFA66Xbz4W5zOmcNOQli7pG16EhXH9DBFNhheSpO8gjC6bq2g_71Jmm0Ksksuyeklee97L-_Lh1DXFwxoGgkiJReEcQYkzjJKgsyoT0UigLrLdxQOJ-x5Gkxdwa10bZUrn2gdtZpLUyPvUaPUHYUaUN8WC2JUo8zrqpPQ2EVN7YK5PufN-8fR69umyuJFkcd8R8zT2XuvqKDQw5dvBFV-haI_9LaVP7ZBZnCI9h06xHf1dh6hHciP0YFDitjdw_IEPb3Dck7A8vaw5QSV-CPHOre1GHSGbWMatizFb2xqrdj0t5NyoU8EYAVrzuIpmgwexw9D4kQRiKScVRoNsxjCCDwfJBM89WXAw1gxRT3JpEmQgpT6kAFVfQ40Zr7w-lkY89QTGpwBPUONfJ7DOcIy9VU_Ap0QgmChl8apCJTiOj-VPFMZtNDNyj6JdD-GG-GKWVK_XNPEGDOpjdlC3fXiov4o4_9l19rQ21e0V5uQuPtUJpvdv9g-fYn2-ibwWrZgGzWq5SdcadhQiY47Gx2bdutx_DL9AZgByYc |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LS8QwEB50PejFt7g-c9CLEGybtE0PIj7Z1XURURAvtUmmICz76orun_I3mvThKog3L710yGEySb6ZzJcPYM-VHFkSSqqUkJQLjjRKU0b91KpPhdLHosu3HTQe-NWj_zgFHxUXxrZVVntivlHrnrI18kNmlbrDwADq4_6AWtUoe7taSWgUYXGN4zeTsmVHzXMzv_ued3lxf9agpaoAVUzwkYGTPMIgRMdFxaVIXOWLINJcM0dxZTMMP2Eupsi0J5BF3JWOlwaRSBxp0A0yM-40zHDLaK3BzOlF-_ZuUtVxwtDhbkkEdCJ22B9h33zeXSvg8u3o-0Gnq_b__FC7XIT5Eo2SkyJ8lmAKu8uwUCJTUq77bAWaTzjsUcx5giTnIGXkpUtMLp1j3g7JG-FIzoocE1vbJbafnmYDE4FINH5xJFfh4V_ctQa1bq-L60BU4movRJOAouSBk0SJ9LUWJh9WItUp1uGg8k-syhfKrVBGJy5uyllsnRkXzqzD3pdxv3iY43ezXePovy22qkmIy_WbxZNo2_j79y7MNu5vWnGr2b7ehDnPHvo5U3ELaqPhK24byDKSO2WcEHj-79D8BFGrA3A |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Zero-energy+states+in+conformal+field+theory+with+sine-square+deformation&rft.jtitle=Progress+of+theoretical+and+experimental+physics&rft.au=Tamura%2C+Shota&rft.au=Katsura%2C+Hosho&rft.date=2017-11-01&rft.issn=2050-3911&rft.eissn=2050-3911&rft.volume=2017&rft.issue=11&rft_id=info:doi/10.1093%2Fptep%2Fptx147&rft.externalDBID=n%2Fa&rft.externalDocID=10_1093_ptep_ptx147 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2050-3911&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2050-3911&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2050-3911&client=summon |