2017/11/30 by Santiago Migliaccio, Sylvain Ribault · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/jhep05(2018)169
27 pages. Python code available at https://github.com/ribault/bootstrap-2d-Python V2: Some clarifications included. Added plot of spectrum
arxiv created 2018/05/25 · arxiv updated 2018/07/04
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.