The analytic bootstrap equations of non-diagonal two-dimensional CFT

Abstract : 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.
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Santiago Migliaccio, Sylvain Ribault. The analytic bootstrap equations of non-diagonal two-dimensional CFT. Journal of High Energy Physics, Springer, 2018, 2018, pp.169. ⟨10.1007/JHEP05(2018)169⟩. ⟨cea-01695664⟩

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