Large spin perturbation theory for conformal field theories
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalized free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quart...
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| Format: | Journal article |
| Language: | English |
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American Physical Society
2017
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| _version_ | 1797078368919748608 |
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| author | Alday, L |
| author_facet | Alday, L |
| author_sort | Alday, L |
| collection | OXFORD |
| description | We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalized free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories around generalized free fields. |
| first_indexed | 2024-03-07T00:30:57Z |
| format | Journal article |
| id | oxford-uuid:7fc9fd05-6313-4a92-9585-a0dd0b6e5bfd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:30:57Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | oxford-uuid:7fc9fd05-6313-4a92-9585-a0dd0b6e5bfd2022-03-26T21:19:08ZLarge spin perturbation theory for conformal field theoriesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7fc9fd05-6313-4a92-9585-a0dd0b6e5bfdEnglishSymplectic Elements at OxfordAmerican Physical Society2017Alday, LWe consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalized free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In such cases the twist conformal blocks can be decomposed into a sequence of functions which we systematically construct. Decomposing the four-point correlator in this basis turns crossing symmetry into an algebraic problem. Our method can be applied to a wide spectrum of conformal field theories in any number of dimensions and at any order in the breaking parameter. As an example, we compute the spectrum of various theories around generalized free fields. |
| spellingShingle | Alday, L Large spin perturbation theory for conformal field theories |
| title | Large spin perturbation theory for conformal field theories |
| title_full | Large spin perturbation theory for conformal field theories |
| title_fullStr | Large spin perturbation theory for conformal field theories |
| title_full_unstemmed | Large spin perturbation theory for conformal field theories |
| title_short | Large spin perturbation theory for conformal field theories |
| title_sort | large spin perturbation theory for conformal field theories |
| work_keys_str_mv | AT aldayl largespinperturbationtheoryforconformalfieldtheories |