Rg Flows in the $D$-Series of Minimal Cfts

Timothy R. Klassen; Ezer Melzer

doi:10.1016/0550-3213(93)90415-L

paper

Rg Flows in the $D$ -Series of Minimal Cfts

arXiv:hep-th/9110047 · doi:10.1016/0550-3213(93)90415-L

Abstract

Using results of the thermodynamic Bethe Ansatz approach and conformal perturbation theory we argue that the $ϕ_{1, 3}$ -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 $\ZZ_2$-even $ϕ_{1, 3}$ -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.

30 pages

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RG flows of non-diagonal minimal models perturbed by $ϕ_{1, 3}$

Rg Flows in the D-Series of Minimal Cfts

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Rg Flows in the $D$ -Series of Minimal Cfts