From Fuchsian differential equations to integrable QFT

V V Bazhanov, S L Lukyanov
2014 Journal of Physics A: Mathematical and Theoretical  
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
more » ... . A detailed account of the results announced in this letter is contained in a separate publication arXiv:1310.4390.
doi:10.1088/1751-8113/47/46/462002 fatcat:5var7fhoofemnmuvoiilletqoe