New families of flows between two-dimensional conformal field theories

TL;DR

This paper uncovers numerous new renormalisation group flows between nonunitary minimal models in 2D conformal field theory, characterized by non-monotonic effective central charge behavior studied via nonlinear integral equations.

Contribution

It introduces multiple new families of flows associated with specific perturbations, extending previous findings and analyzing their non-monotonic central charge evolution.

Findings

Discovery of infinitely-many new RG flow families

Non-monotonic effective central charge in these flows

Application of nonlinear integral equations to study flow dynamics

Abstract

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 $\phi_{21}$ and $\phi_{15}$ 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 $\phi_{13}$ perturbations, when the flows induced are between nonunitary minimal models.