  We establish an intriguing correspondence between a special set of classical
solutions of the modified sinh-Gordon equation (i.e., Hitchin's "self-duality"
equations) on a punctured Riemann sphere and a set of stationary states in the
finite-volume Hilbert space of the integrable 2D QFT introduced by V.A. Fateev.
Potential applications of this correspondence to the problem of
non-perturbative quantization of classically integrable non-linear sigma models
are briefly discussed. A detailed account of the results announced in this
letter is contained in a separate publication arXiv:1310.4390.
