High energy QCD as a completely integrable model

http://www.physik.uni-regensburg.de/forschung/hep_data/braun/selected_talks/uses.pdf

The Uses of conformal symmetry in QCD

Baryon distribution amplitudes in QCD

Gauge/string duality for QCD conformal operators

We define and study certain integrable lattice models with non-compact quantum group symmetry (the modular double of ) including an integrable lattice regularization of the sinh-Gordon model and a non-compact version of the XXZ model. Their fundamental R-matrices are constructed in terms of the non-compact quantum dilogarithm. Our choice of the quantum group representations naturally ensures self-adjointness of the Hamiltonian and the higher integrals of motion. These models are studied with the help of the separation of variables method. We show that the spectral problem for the integrals of motion can be reformulated as the problem to determine a subset among the solutions to certain finite difference equations (Baxter equation and quantum Wronskian equation) which is characterized by suitable analytic and asymptotic properties. A key technical tool is the so-called -operator, for which we give an explicit construction. Our results allow us to establish some connections to related results and conjectures on the sinh-Gordon theory in continuous spacetime. Our approach also sheds some light on the relations between massive and massless models (in particular, the sinh-Gordon and Liouville theories) from the point of view of their integrable structures.

https://www.pdmi.ras.ru/~bytsko/repr/jpa39.pdf

Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model

This paper discusses a method of constructing local Hamiltonians for integrable lattice models proposed by Tarasov, Takhtadzhyan, and Faddeev. The method is generalized to the case of inhomogeneous models. Another model, inhomogeneous, is considered which describes the interaction of spin impurities with a model of the type of a nonlinear lattice Schroedinger model.

V. O. Tarasov

Papers

Local Hamiltonians for integrable quantum models on a lattice. II