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

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

2010-05-23

arxiv.org/abs/1005.4199v3

SIGMA 6 (2010), 085, 34 pages

Mathematics

Quantum Algebra

Scientific paper

10.3842/SIGMA.2010.085

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.

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