Identify the ultraviolet CFT for the diagonal mixed-chirality solution

Identify, for each integer n>1, a conformal field theory whose effective central charge is n(2n+1)/(2n+3) and whose operator content is compatible with the regular ultraviolet plateau of the diagonal mixed-chirality amplitude S^{RL}_{ab}(\theta)=S_{ab}^{-1}(\theta).

Background

The paper classifies several pole-free mixed-chirality solutions of the A_{2n}^{(2)} massless S-matrix bootstrap. The diagonal solution, obtained by taking the inverse of the massive same-chirality amplitudes, has a regular constant Y-system solution and an ultraviolet effective central charge n(2n+1)/(2n+3).

For n=1,2,3 the associated Y-systems have a regular periodicity consistent with a perturbing chiral dimension h_diag=3/4. However, for general n>1, the authors do not identify a conformal field theory simultaneously realizing the computed effective central charge and the required operator content. Determining that ultraviolet theory would complete the interpretation of this algebraically consistent massless scattering solution as an RG flow.