SciPost Submission Page
Algebraic structure of classical integrability for complex sine-Gordon
by J. Avan, L. Frappat, E. Ragoucy
|As Contributors:||Luc FRAPPAT|
|Submitted by:||FRAPPAT, Luc|
|Submitted to:||SciPost Physics|
|Subject area:||Mathematical Physics|
The algebraic structure underlying the classical $r$-matrix formulation of the complex sine-Gordon model is fully elucidated. It is characterized by two matrices $a$ and $s$, components of the $r$ matrix as $r=a-s$. They obey a modified classical reflection/Yang--Baxter set of equations, further deformed by non-abelian dynamical shift terms along the dual Lie algebra $su(2)^*$. 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.