New families of flows between two-dimensional conformal field theories

We present evidence for the existence of infinitely-many new families of renormalisation group flows between the nonunitary minimal models of conformal field theory. These are associated with perturbations by the ${\varphi }_{21}$ and ${\varphi }_{15}$ operators, and generalise a family of flows discovered by Martins. In all of the new flows, the finite-volume effective central charge is a non-monotonic function of the system size. The evolution of this effective central charge is studied by means of a nonlinear integral equation, a massless variant of an equation recently found to describe certain massive perturbations of these same models. We also observe that a similar non-monotonicity arises in the more familiar ${\varphi }_{13}$ perturbations, when the flows induced are between nonunitary minimal models.