Abstract
The algebraic structure underlying the classical rr-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices aa and ss, components of the rr matrix as r=a-sr=a−s. They obey a modified classical reflection/Yang–Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra su(2)^*su(2)*. The sign shift pattern of this deformation has the signature of the twisted boundary dynamical algebra. Issues related to the quantization of this algebraic structure and the formulation of quantum complex sine-Gordon on those lines are introduced and discussed.
Highlights
The complex sine-Gordon (CSG) field theory is a two-dimensional relativistic model with U(1) symmetry, exhibiting classical and quantum integrability features
An alternative Lagrangian using a different set of fields was proposed by Getmanov [3] and the corresponding Lax pair was derived by De Vega and Maillet [4]
A later interpretation of the CSG model as a coset SU(2)/U(1) WZW model perturbed by thermal operator was derived by Bakas [5]
Summary
The complex sine-Gordon (CSG) field theory is a two-dimensional relativistic model with U(1) symmetry, exhibiting classical and quantum integrability features. One lacks in particular an algebraic formulation of the r-matrix structure for the classical Lax matrix, useful to define a quantum model preserving at least some features of integrability through its derived algebraic structure. It may help understanding the integrability breaking mechanism and its subsequent restoring. A starting point to achieve such a quantum formulation is to completely unravel the classical Hamiltonian formulation by r-matrix formalism proposed by Maillet [8] This known r-matrix exhibits characteristic features of a dynamical structure, albeit not of Gervais–Neveu– Felder type (abelian dynamical structure) [9, 10].
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