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

Abstract

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.

References in corpus (4)

• Cluster algebras via cluster categories with infinite-dimensional morphism spaces
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras I: Type B_r
• Periodicities of T and Y-systems, dilogarithm identities, and cluster algebras II: Types C_r, F_4, and G_2
• Dilogarithm identities for conformal field theories and cluster algebras: simply laced case

Cited by in corpus (3)

• Classical and Quantum Dilogarithm Identities
• Periodicities in cluster algebras and dilogarithm identities
• Classical and Quantum Dynamics on Orbifolds