Abstract
We establish an intriguing correspondence between a special set of classical solutions of the modified sinh-Gordon equation (i.e., Hitchins '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).
Original language | English (US) |
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Article number | 462002 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 47 |
Issue number | 46 |
DOIs | |
State | Published - Nov 21 2014 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- General Physics and Astronomy
Keywords
- Fuchsian differential equations
- classical integrable equations
- integrable systems
- quantum field theory