%0 Journal Article %T The analytic bootstrap equations of non-diagonal two-dimensional CFT %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %A Migliaccio, Santiago %A Ribault, Sylvain %< avec comité 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