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

By A. Bytsko, J. Teschner. 2006

164 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ee7bac8b5f38f6b80708f037bdc0682bf8de7402

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Citations in the corpus

N=2 supersymmetric theories on squashed three-sphere (2011, unknown): “(149) In the region |y| < 1/v, the function fb(z) is given by[26, 27] fb(z) ≡ log sb(z) = iπ ( z(2) 2 + b(2) + b 24 ) + ∫”
Notes on SUSY gauge theories on three-sphere (2010, methodology): “8) For more detailed explanation on this function, we refer to [17, 18].”
Quantum Riemann Surfaces in Chern-Simons Theory (2011, background): “Properties of this remarkable function have been discussed in many places, including [75, 19, 76, 77, 78, 79, 80, 2].”
The gravity dual of supersymmetric gauge theories on a squashed three-sphere (2011, background): “20) Here fb(z) − f asymp b (z) has the property that it tends to zero as |Re z| → ∞ [42, 43].”
SUSY gauge theories on squashed three-spheres (2011, background): “See [20, 21] for more details on this function.”