Abstract
We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinh-Gordon equation arise in this case as a zero-curvature condition for a class of multivalued connections on the punctured Riemann sphere, similarly to Hitchin’s self-duality equations. The proposed correspondence between the classical and quantum integrable systems provides a powerful tool for deriving functional and integral equations which determine the full spectrum of local integrals of motion for massive QFT in a finite volume. Potential applications of our results to the problem of non-perturbative quantization of classically integrable non-linear sigma models are briefly discussed.
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Bazhanov, V.V., Lukyanov, S.L. Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states. J. High Energ. Phys. 2014, 147 (2014). https://doi.org/10.1007/JHEP09(2014)147
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DOI: https://doi.org/10.1007/JHEP09(2014)147