From Fuchsian differential equations to integrable QFT

We establish an intriguing correspondence between a special set of classical solutions of the modified sinh-Gordon equation (i.e., Hitchinʼs 'self-duality' equations) on a punctured Riemann sphere and a set of stationary states in the finite-volume Hilbert space of the integrable 2D quantu...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2014-11, Vol.47 (46), p.462002
Main Authors: Bazhanov, V V, Lukyanov, S L
Format: Article
Language:English
Subjects:
classical integrable equations
Fuchsian differential equations
integrable systems
quantum field theory
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Summary:We establish an intriguing correspondence between a special set of classical solutions of the modified sinh-Gordon equation (i.e., Hitchinʼs 'self-duality' equations) on a punctured Riemann sphere and a set of stationary states in the finite-volume Hilbert space of the integrable 2D quantum field theory introduced by VA Fateev. An application of this correspondence to the problem of non-perturbative 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 [hep-th] and Bazhanov et al 2014 J. High Energy Phys. JHEP09(2014)147).
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/47/46/462002