Integrable structure of Quantum Field Theory: classical flat connections versus quantum stationary states
Abstract
We establish a correspondence between an infinite set of special solutions of the (classical) modified sinhGordon equation and a set of stationary states in the finitevolume Hilbert space of the integrable 2D QFT invented by V.A. Fateev. The modified sinhGordon equation arise in this case as a zerocurvature condition for a class of multivalued connections on the punctured Riemann sphere, similarly to Hitchin's selfduality 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 nonperturbative quantization of classically integrable nonlinear sigma models are briefly discussed.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2014
 DOI:
 10.1007/JHEP09(2014)147
 arXiv:
 arXiv:1310.4390
 Bibcode:
 2014JHEP...09..147B
 Keywords:

 Field Theories in Lower Dimensions;
 Integrable Field Theories;
 Integrable Hierarchies;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 63 pages, 8 figures