%0 Journal Article
%T The analytic bootstrap equations of non-diagonal two-dimensional CFT
%+ Institut de Physique ThÃ©orique - UMR CNRS 3681 (IPHT)
%A Migliaccio, Santiago
%A Ribault, Sylvain
%< avec comitÃ© de lecture
%Z t17/203
%@ 1126-6708
%J Journal of High Energy Physics
%I Springer
%V 2018
%P 169
%8 2018-05-28
%D 2018
%Z 1711.08916
%R 10.1007/JHEP05(2018)169
%K High Energy Physics - Theory (hep-th)
%Z Physics [physics]Journal articles
%X Under the assumption that degenerate fields exist, diagonal CFTs such as Liouville theory can be solved analytically using the conformal bootstrap method. Here we generalize this approach to non-diagonal CFTs, i.e. CFTs whose primary fields have nonzero conformal spins. Assuming generic values of the central charge, we find that the non-diagonal sector of the spectrum must be parametrized by two integer numbers. We then derive and solve the equations that determine how three-and four-point structure constants depend on these numbers. In order to test these results, we numerically check crossing symmetry of a class of four-point functions in a non-rational limit of D-series minimal models. The simplest four-point functions in this class were previously argued to describe connectivities of clusters in the critical Potts model.
%G English
%2 https://cea.hal.science/cea-01695664/document
%2 https://cea.hal.science/cea-01695664/file/1711.08916.pdf
%L cea-01695664
%U https://cea.hal.science/cea-01695664
%~ CEA
%~ CNRS
%~ DSM-IPHT
%~ CEA-UPSAY
%~ UNIV-PARIS-SACLAY
%~ CEA-UPSAY-SACLAY
%~ CEA-DRF
%~ TEST-HALCNRS
%~ GS-MATHEMATIQUES
%~ GS-PHYSIQUE