1d conformal field theory and dispersion relations
Abstract We study conformal field theory in d = 1 space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of [1], which holds for CFTs in dimensi...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)119 |
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| author | Dean Carmi Sudip Ghosh Trakshu Sharma |
| author_facet | Dean Carmi Sudip Ghosh Trakshu Sharma |
| author_sort | Dean Carmi |
| collection | DOAJ |
| description | Abstract We study conformal field theory in d = 1 space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of [1], which holds for CFTs in dimensions d ≥ 2, to the case of d = 1. The dispersion relation is obtained by combining the Lorentzian inversion formula with the operator product expansion of the 4-point correlator. We perform checks of the dispersion relation using correlators of generalised free fields and derive an integral relation between the kernel of the dispersion relation and that of the Lorentzian inversion formula. Finally, for 1-d holographic conformal theories, we analytically compute scalar Witten diagrams in AdS 2 at tree-level and 1-loop. |
| format | Article |
| id | doaj-art-7c7420bb3b734bd0b0ce26b9ec0514d9 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-7c7420bb3b734bd0b0ce26b9ec0514d92025-01-05T12:06:10ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213310.1007/JHEP12(2024)1191d conformal field theory and dispersion relationsDean Carmi0Sudip Ghosh1Trakshu Sharma2Department of Mathematics and Physics University of Haifa at OranimDepartment of Physics and Haifa Center for Physics and Astrophysics, University of HaifaDepartment of Physics and Haifa Center for Physics and Astrophysics, University of HaifaAbstract We study conformal field theory in d = 1 space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of [1], which holds for CFTs in dimensions d ≥ 2, to the case of d = 1. The dispersion relation is obtained by combining the Lorentzian inversion formula with the operator product expansion of the 4-point correlator. We perform checks of the dispersion relation using correlators of generalised free fields and derive an integral relation between the kernel of the dispersion relation and that of the Lorentzian inversion formula. Finally, for 1-d holographic conformal theories, we analytically compute scalar Witten diagrams in AdS 2 at tree-level and 1-loop.https://doi.org/10.1007/JHEP12(2024)119Field Theories in Lower DimensionsScale and Conformal Symmetries |
| spellingShingle | Dean Carmi Sudip Ghosh Trakshu Sharma 1d conformal field theory and dispersion relations Journal of High Energy Physics Field Theories in Lower Dimensions Scale and Conformal Symmetries |
| title | 1d conformal field theory and dispersion relations |
| title_full | 1d conformal field theory and dispersion relations |
| title_fullStr | 1d conformal field theory and dispersion relations |
| title_full_unstemmed | 1d conformal field theory and dispersion relations |
| title_short | 1d conformal field theory and dispersion relations |
| title_sort | 1d conformal field theory and dispersion relations |
| topic | Field Theories in Lower Dimensions Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP12(2024)119 |
| work_keys_str_mv | AT deancarmi 1dconformalfieldtheoryanddispersionrelations AT sudipghosh 1dconformalfieldtheoryanddispersionrelations AT trakshusharma 1dconformalfieldtheoryanddispersionrelations |