Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems

Symmetry Integrability and Geometry-Methods and Applications

article

Tomoki Nakanishi¹  Roberto Tateo² 

[1] Graduate School of Mathematics, Nagoya University;Dipartimento di Fisica Teorica and INFN

关键词: cluster algebras;    quantum groups;    integrable models;   

DOI  :  10.3842/SIGMA.2010.085

来源: National Academy of Science of Ukraine

【 摘 要 】

We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.

【 授权许可】

Unknown