RG Flows in the D-Series of Minimal CFTs

Using results of the thermodynamic Bethe Ansatz approach and conformal perturbation theory we argue that the φ1,3-perturbation of a unitary minimal (1 + 1)-dimensional conformal field theory (CFT) in the D-series of modular invariant partition functions induces a renormalization group (RG) flow to the next-lower model in the D-series. An exception is the first model in the series, the 3-state Potts CFT, which under the Z2-even φ1,3-perturbation flows to the tricritical Ising CFT, the second model in the A-series. We present arguments that in the A-series flow corresponding to this exceptional case, interpolating between the tetracritical and the tricritical Ising CFT, the IR fixed point is approached from “exactly the opposite direction”. Our results indicate how (most of) the relevant conformal fields evolve from the UV to the IR CFT.