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...

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Main Authors: Alday, L, Henriksson, J, Van Loon, M
Formato: Journal article
Publicado: Springer 2018
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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.
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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