Analytic bounds and emergence of AdS2 physics from the conformal bootstrap
Abstract We study analytically the constraints of the conformal bootstrap on the lowlying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we u...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-04-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | http://link.springer.com/article/10.1007/JHEP04(2017)146 |
| _version_ | 1818328101505990656 |
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| author | Dalimil Mazáč |
| author_facet | Dalimil Mazáč |
| author_sort | Dalimil Mazáč |
| collection | DOAJ |
| description | Abstract We study analytically the constraints of the conformal bootstrap on the lowlying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension. We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry. When the external scaling dimensions are large, our functionals provide a direct point of contact between crossing in a 1D CFT and scattering of massive particles in large AdS2. In particular, CFT crossing can be shown to imply that appropriate OPE coefficients exhibit an exponential suppression characteristic of massive bound states, and that the 2D flat-space S-matrix should be analytic away from the real axis. |
| first_indexed | 2024-12-13T12:26:49Z |
| format | Article |
| id | doaj.art-31f4662c362d494eb175c2a0eed876c0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T12:26:49Z |
| publishDate | 2017-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-31f4662c362d494eb175c2a0eed876c02022-12-21T23:46:16ZengSpringerOpenJournal of High Energy Physics1029-84792017-04-012017414410.1007/JHEP04(2017)146Analytic bounds and emergence of AdS2 physics from the conformal bootstrapDalimil Mazáč0Perimeter Institute for Theoretical PhysicsAbstract We study analytically the constraints of the conformal bootstrap on the lowlying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension. We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry. When the external scaling dimensions are large, our functionals provide a direct point of contact between crossing in a 1D CFT and scattering of massive particles in large AdS2. In particular, CFT crossing can be shown to imply that appropriate OPE coefficients exhibit an exponential suppression characteristic of massive bound states, and that the 2D flat-space S-matrix should be analytic away from the real axis.http://link.springer.com/article/10.1007/JHEP04(2017)146AdS-CFT CorrespondenceConformal Field TheoryScattering AmplitudesField Theories in Lower Dimensions |
| spellingShingle | Dalimil Mazáč Analytic bounds and emergence of AdS2 physics from the conformal bootstrap Journal of High Energy Physics AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes Field Theories in Lower Dimensions |
| title | Analytic bounds and emergence of AdS2 physics from the conformal bootstrap |
| title_full | Analytic bounds and emergence of AdS2 physics from the conformal bootstrap |
| title_fullStr | Analytic bounds and emergence of AdS2 physics from the conformal bootstrap |
| title_full_unstemmed | Analytic bounds and emergence of AdS2 physics from the conformal bootstrap |
| title_short | Analytic bounds and emergence of AdS2 physics from the conformal bootstrap |
| title_sort | analytic bounds and emergence of ads2 physics from the conformal bootstrap |
| topic | AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes Field Theories in Lower Dimensions |
| url | http://link.springer.com/article/10.1007/JHEP04(2017)146 |
| work_keys_str_mv | AT dalimilmazac analyticboundsandemergenceofads2physicsfromtheconformalbootstrap |