From Fuchsian differential equations to integrable QFT

Abstract

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 account of the results announced in this letter is contained in a separate publication arXiv:1310.4390.

4 pages, 1 figure, v2: minor corrections

References in corpus (2)

• The ODE/IM Correspondence
• Integrable structure of Quantum Field Theory: Classical flat connections versus quantum stationary states

Cited by in corpus (3)

• Geometric aspects of the ODE/IM correspondence
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• Massive ODE/IM Correspondence and Non-linear Integral Equations for $A_r^{(1)}$-type modified Affine Toda Field Equations