Taming the ϵ-expansion with large spin perturbation theory
We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an ϵ-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recentl...
| Main Authors: | , , |
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| Format: | Journal article |
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Springer
2018
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| _version_ | 1826292902100205568 |
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| author | Alday, L Henriksson, J Van Loon, M |
| author_facet | Alday, L Henriksson, J Van Loon, M |
| author_sort | Alday, L |
| collection | OXFORD |
| description | We apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an ϵ-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recently proposed Froissart-Gribov inversion integral, then allows one to reconstruct the CFT data of intermediate operators of any spin. We use this method to compute the anomalous dimensions and OPE coefficients of leading twist operators. To cubic order in ϵ the double discontinuity arises solely from the identity operator and the scalar bilinear operator, making the computation straightforward. At higher orders the double discontinuity receives contributions from infinite towers of higher spin operators. At fourth order, the structure of perturbation theory leads to a proposal in terms of functions of certain degree of transcendentality, which can then be fixed by symmetries. This leads to the full determination of the CFT data for leading twist operators to fourth order. |
| first_indexed | 2024-03-07T03:21:51Z |
| format | Journal article |
| id | oxford-uuid:b7b16ea8-bfad-44fa-9c98-beef9e65b215 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:21:51Z |
| publishDate | 2018 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:b7b16ea8-bfad-44fa-9c98-beef9e65b2152022-03-27T04:50:29ZTaming the ϵ-expansion with large spin perturbation theoryJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b7b16ea8-bfad-44fa-9c98-beef9e65b215Symplectic Elements at OxfordSpringer2018Alday, LHenriksson, JVan Loon, MWe apply analytic bootstrap techniques to the four-point correlator of fundamental fields in the Wilson-Fisher model. In an ϵ-expansion crossing symmetry fixes the double discontinuity of the correlator in terms of CFT data at lower orders. Large spin perturbation theory, or equivalently the recently proposed Froissart-Gribov inversion integral, then allows one to reconstruct the CFT data of intermediate operators of any spin. We use this method to compute the anomalous dimensions and OPE coefficients of leading twist operators. To cubic order in ϵ the double discontinuity arises solely from the identity operator and the scalar bilinear operator, making the computation straightforward. At higher orders the double discontinuity receives contributions from infinite towers of higher spin operators. At fourth order, the structure of perturbation theory leads to a proposal in terms of functions of certain degree of transcendentality, which can then be fixed by symmetries. This leads to the full determination of the CFT data for leading twist operators to fourth order. |
| spellingShingle | Alday, L Henriksson, J Van Loon, M Taming the ϵ-expansion with large spin perturbation theory |
| title | Taming the ϵ-expansion with large spin perturbation theory |
| title_full | Taming the ϵ-expansion with large spin perturbation theory |
| title_fullStr | Taming the ϵ-expansion with large spin perturbation theory |
| title_full_unstemmed | Taming the ϵ-expansion with large spin perturbation theory |
| title_short | Taming the ϵ-expansion with large spin perturbation theory |
| title_sort | taming the ϵ expansion with large spin perturbation theory |
| work_keys_str_mv | AT aldayl tamingtheeexpansionwithlargespinperturbationtheory AT henrikssonj tamingtheeexpansionwithlargespinperturbationtheory AT vanloonm tamingtheeexpansionwithlargespinperturbationtheory |