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Title: Wonder of sine-gordon Y -systems
Authors: Nakanishi, Tomoki
Stella, Salvatore
First Published: 22-Jan-2016
Publisher: American Mathematical Society
Citation: Transactions of the American Mathematical Society, 2016, 368 (10), pp. 6835-6886
Abstract: The sine-Gordon Y -systems and the reduced sine-Gordon Y - systems were introduced by Tateo in the 1990’s in the study of the integrable deformation of conformal field theory by the thermodynamic Bethe ansatz method. The periodicity property and the dilogarithm identities concerning these Y -systems were conjectured by Tateo, and only a part of them have been proved so far. In this paper we formulate these Y -systems by the polygon realization of cluster algebras of types A and D and prove the conjectured periodicity and dilogarithm identities in full generality. As it turns out, there is a wonderful interplay among continued fractions, triangulations of polygons, cluster algebras, and Y -systems.
DOI Link: 10.1090/tran/6505
ISSN: 0002-9947
Version: Post-print
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2016, American Mathematical Society. Deposited with reference to the publisher’s open access archiving policy. (
Appears in Collections:Published Articles, Dept. of Mathematics

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