Nagoya Mathematical Journal

Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case

Tomoki Nakanishi

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Abstract

The dilogarithm identities for the central charges of conformal field theories of simply laced type were conjectured by Bazhanov, Kirillov, and Reshetikhin. Their functional generalizations were conjectured by Gliozzi and Tateo. They have been partly proved by various authors. We prove these identities in full generality for any pair of Dynkin diagrams of simply laced type based on the cluster algebra formulation of the Y-systems.

Article information

Source
Nagoya Math. J., Volume 202 (2011), 23-43.

Dates
First available in Project Euclid: 31 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1306851588

Digital Object Identifier
doi:10.1215/00277630-1260432

Mathematical Reviews number (MathSciNet)
MR2804544

Zentralblatt MATH identifier
1284.81157

Subjects
Primary: 13F60: Cluster algebras
Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Citation

Nakanishi, Tomoki. Dilogarithm identities for conformal field theories and cluster algebras: Simply laced case. Nagoya Math. J. 202 (2011), 23--43. doi:10.1215/00277630-1260432. https://projecteuclid.org/euclid.nmj/1306851588


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