Classify ultraviolet-complete higher mixed-chirality bootstrap solutions

Establish which remaining folded A_{2n}^{(2)} mixed-chirality scattering amplitudes admit regular conformal ultraviolet limits, and prove whether the minimal and diagonal amplitudes are the only elementary solutions with ultraviolet completeness, while the higher solutions encounter a singularity before reaching the ultraviolet regime.

Background

The folded A_{2n}^{(2)} bootstrap equations possess elementary solutions labelled by k=1,...,n, as well as products such as the saturated amplitude. Algebraic bootstrap consistency alone does not ensure a conventional ultraviolet conformal limit: the saturated solution has no positive real constant Y-system solution, and preliminary investigations suggest analogous behavior for the remaining higher solutions.

The authors explicitly formulate a conjecture that only the minimal and diagonal elementary amplitudes admit regular conformal ultraviolet limits. A systematic analysis of the remaining solutions is left unresolved, including establishing the proposed classification and determining whether the higher solutions necessarily develop singularities before the ultraviolet regime.