From Fuchsian differential equations to integrable QFT
Abstract
We establish an intriguing correspondence between a special set of classical solutions of the modified sinhGordon equation (i.e., Hitchin's ‘selfduality’ equations) on a punctured Riemann sphere and a set of stationary states in the finitevolume Hilbert space of the integrable 2D quantum field theory introduced by VA Fateev. An application of this correspondence to the problem of nonperturbative quantization of classically integrable nonlinear sigma models is briefly discussed. A detailed account of the results announced in this communication is contained in separate publications (Bazhanov and Lukyanov 2014 arXiv:1310.4390 [hepth] and Bazhanov et al 2014 J. High Energy Phys. JHEP09(2014)147).
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2014
 DOI:
 10.1088/17518113/47/46/462002
 arXiv:
 arXiv:1310.8082
 Bibcode:
 2014JPhA...47T2002B
 Keywords:

 Mathematical Physics;
 High Energy Physics  Theory
 EPrint:
 4 pages, 1 figure, v2: minor corrections