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arXiv:2608.24385

New RG flows between non-Unitary CFTs from exact massless scattering theories

Changrim Ahn, Zoltán Bajnok, Soma Elek

Published Aug 25, 2026• 0 citations
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Abstract

We construct complete solutions of the massless S-matrix bootstrap equations describing a new infinite family of integrable RG flows from the higher-fusion-level minimal models M(3,2n+3;n) to the non-unitary Virasoro minimal models M(2,2n+3), including a flow from M(3,5) to the Yang--Lee CFT M(2,5) when n=1. We provide strong evidence for this identification by matching conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations. We further show that a family of non-invertible Verlinde defect lines is preserved along the flows.

DOI
10.48550/arxiv.2608.24385

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We construct complete solutions of the massless S-matrix bootstrap equations describing a new infinite family of integrable RG flows from the higher-fusion-level minimal models M(3,2n+3;n) to the non-unitary Virasoro minimal models M(2,2n+3), including a flow from M(3,5) to the Yang--Lee CFT M(2,5) when n=1. We provide strong evidence for this identification by matching conformal perturbation theory around the UV fixed points with the small-volume expansion of the corresponding thermodynamic Bethe ansatz equations. We further show that a family of non-invertible Verlinde defect lines is preserved along the flows.
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We consider the non-unitary Lee-Yang minimal model M(2,  5) \mathrm{\mathcal{M}}\left(2,\;5\right) M(2,5) in three different finite geometries: (i) on the interval with integrable boundary conditions labelled by the Kac labels (r, s) = (1, 1), (1, 2), (ii) on the circle with periodic boundary conditions and (iii) on the periodic circle including an integrable purely transmitting defect. We apply φ1,3 integrable perturbations on the boundary and on the defect and describe the flow of the spectrum. Adding a Φ1,3 integrable perturbation to move off-criticality in the bulk, we determine the finite size spectrum of the massive scattering theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations. We derive these integral equations for all excitations by solving, in the continuum scaling limit, the TBA functional equations satisfied by the transfer matrices of the associated A4 RSOS lattice model of Forrester and Baxter in Regime III. The excitations are classified in terms of (m, n) systems. The excited state TBA equations agree with the previously conjectured equations in the boundary and periodic cases. In the defect case, new TBA equations confirm previously conjectured transmission factors.
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We present a full classification of UV complete QFTs that RG flow to the 2D Ising CFT by solving the bootstrap equations for massless right--left S-matrices. For the Ising model with E_8 spectrum, we find exactly four completions, arising from higher-T\bar T-type deformations, including a previously unknown ``golden flow'' whose UV fixed point is a diagonal su(2) coset CFT (c=25/14) along Δ_{\rm rel}=2/7. A universal Fibonacci/E_8 structure governs the R--L adjacency matrices and the Y-system periods, so that the E_8 symmetry persists across all RG scales.