Anomalous dimensions at finite conformal spin from OPE inversion
Abstract We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of [1], both from the position space representation as well as from the integral viz. Mellin representation of the conformal blocks. The Me...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP11(2018)052 |
| _version_ | 1818696026668662784 |
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| author | Carlos Cardona Kallol Sen |
| author_facet | Carlos Cardona Kallol Sen |
| author_sort | Carlos Cardona |
| collection | DOAJ |
| description | Abstract We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of [1], both from the position space representation as well as from the integral viz. Mellin representation of the conformal blocks. The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform. We evaluate the contributions of scalar and spin exchanges in the t-channel exactly, in terms of higher order Hypergeometric functions. These relate to a particular exchange of conformal spin β = Δ + J in the s-channel through the inversion formula. Our results reproduce the special cases for large spin anomalous dimension and OPE coefficients obtained previously in the literature. |
| first_indexed | 2024-12-17T13:54:49Z |
| format | Article |
| id | doaj.art-713c7e2d6c3949199f7005e2ac182de5 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-17T13:54:49Z |
| publishDate | 2018-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-713c7e2d6c3949199f7005e2ac182de52022-12-21T21:45:57ZengSpringerOpenJournal of High Energy Physics1029-84792018-11-0120181113610.1007/JHEP11(2018)052Anomalous dimensions at finite conformal spin from OPE inversionCarlos Cardona0Kallol Sen1Niels Bohr International Academy and Discovery Center, University of Copenhagen, Niels Bohr InstituteNiels Bohr International Academy and Discovery Center, University of Copenhagen, Niels Bohr InstituteAbstract We compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of [1], both from the position space representation as well as from the integral viz. Mellin representation of the conformal blocks. The Mellin space is advantageous over the position space not only in allowing to write expressions agnostic to the space-time dimension, but also in that it replaces tedious recursion relations in terms of simple sums which are easy to perform. We evaluate the contributions of scalar and spin exchanges in the t-channel exactly, in terms of higher order Hypergeometric functions. These relate to a particular exchange of conformal spin β = Δ + J in the s-channel through the inversion formula. Our results reproduce the special cases for large spin anomalous dimension and OPE coefficients obtained previously in the literature.http://link.springer.com/article/10.1007/JHEP11(2018)0521/N ExpansionAdS-CFT CorrespondenceConformal Field TheoryScattering Amplitudes |
| spellingShingle | Carlos Cardona Kallol Sen Anomalous dimensions at finite conformal spin from OPE inversion Journal of High Energy Physics 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| title | Anomalous dimensions at finite conformal spin from OPE inversion |
| title_full | Anomalous dimensions at finite conformal spin from OPE inversion |
| title_fullStr | Anomalous dimensions at finite conformal spin from OPE inversion |
| title_full_unstemmed | Anomalous dimensions at finite conformal spin from OPE inversion |
| title_short | Anomalous dimensions at finite conformal spin from OPE inversion |
| title_sort | anomalous dimensions at finite conformal spin from ope inversion |
| topic | 1/N Expansion AdS-CFT Correspondence Conformal Field Theory Scattering Amplitudes |
| url | http://link.springer.com/article/10.1007/JHEP11(2018)052 |
| work_keys_str_mv | AT carloscardona anomalousdimensionsatfiniteconformalspinfromopeinversion AT kallolsen anomalousdimensionsatfiniteconformalspinfromopeinversion |