Dilogarithm identities for sine-Gordon and reduced sine-Gordon Y-Systems

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volumn 6, Issue , 2010, Pages

  Nakanishi, Tomoki ^a   Tateo, Roberto ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Cluster algebras; Integrable models; Quantum groups

Indexed keywords

EID: 84896060731     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2010.085     Document Type: Article

References (36)

1. Baxter R.J., Exactly solved models in statistical mechanics, Academic Press, Inc., London, 1982.
2. Bazhanov V.V., Reshetikhin N., Restricted solid-on-solid models connected with simply laced algebras and conformal field theory, J. Phys. A: Math. Gen. 23 (1990), 1477-1492.
3. Belavin A.A., Polyakov A.M., Zamolodchikov A.B., Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B 241 (1984), 333-380.
4. Bernard D., LeClair A., Residual quantum symmetries of the restricted sine-Gordon theories, Nuclear Phys. B 340 (1990), 721-751.
5. Chapoton F., Functional identities for the Rogers dilogarithm associated to cluster Y-systems, Bull. London Math. Soc. 37 (2005), 755-760.
6. Derksen H., Weyman J., Zelevinsky A., Quivers with potentials and their representations. II. Applications to cluster algebras, J. Amer. Math. Soc. 23 (2010), 749-790, arXiv:0904.0676.
7. Fomin S., Zelevinsky A., Cluster algebras. I. Foundations, J. Amer. Math. Soc. 15 (2002), 497-529, math.RT/0104151.
8. Fomin S., Zelevinsky A., Cluster algebras. II. Finite type classification, Invent. Math. 154 (2003), 63-121, math.RA/0208229.
9. Fomin S., Zelevinsky A., Y-systems and generalized associahedra, Ann. of Math. (2) 158 (2003), 977-1018, hep-th/0111053.
10. Fomin S., Zelevinsky A., Cluster algebras. IV. Coefficients, Compos. Math. 143 (2007), 112-164, math.RT/0602259.
11. Frenkel E., Szenes A., Thermodynamic Bethe ansatz and dilogarithm identities. I, Math. Res. Lett. 2 (1995), 677-693, hep-th/9506215.
12. Gliozzi F., Tateo R., ADE functional dilogarithm identities and integrable models, Phys. Lett. B 348 (1995), 677-693, hep-th/9411203.
13. r, arXiv:1001.1880.
14. 2, arXiv:1001.1881.
15. Inoue R., Iyama O., Kuniba A., Nakanishi T., Suzuki J., Periodicities of T and Y-systems, Nagoya Math. J. 197 (2010), 59-174, arXiv:0812.0667.
16. Keller B., Cluster algebras, quiver representations and triangulated categories, in Triangulated Categories, Editors T. Holm, P. Jørgensen and R. Rouquier, Lecture Note Series, Vol. 375, London Mathematical Society, Cambridge University Press, 2010, 76-160, arXiv:0807.1960.
17. Keller B., The periodicity conjecture for pairs of Dynkin diagrams, arXiv:1001.1531.
18. Kirillov A.N., Reshetikhin N.Y., Exact solution of the Heisenberg XXZ model of spin s, J. Soviet Math. 35 (1986), 2627-2643.
19. Kirillov A.N., Reshetikhin N.Y., Representations of Yangians and multiplicities of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras, J. Soviet Math. 52 (1990), 3156-3164.
20. Klassen T.R., Melzer E., Purely elastic scattering theories and their ultraviolet limits, Nuclear Phys. B 338 (1990), 485-528.
21. Klümper A., Pearce P.A., Conformal weights of RSOS lattice models and their fusion hierarchies, Phys. A 183 (1992), 304-350.
22. (1) r) Bethe ansatz system with q a root of unity, Nuclear Phys. B 389 (1993), 209-244.
23. Kuniba A., Nakanishi T., Spectra in conformal field theories from the Rogers dilogarithm, Modern Phys. Lett. A 7 (1992), 3487-3494, hep-th/9206034.
24. Kuniba A., Nakanishi T., Suzuki J., Functional relations in solvable lattice models. I. Functional relations and representation theory, Internat. J. Modern Phys. A 9 (1994), 5215-5266, hep-th/9309137.
25. Lewin L., Polylogarithms and associated functions, North-Holland, Amsterdam, 1981.
26. Nakanishi T., Dilogarithm identities for conformal field theories and cluster algebras: simply laced case, Nagoya Math. J., to appear, arXiv:0909.5480.
27. Onsager L., Crystal statistics. I. A two-dimensional model with an order disorder transition, Phys. Rev. 65 (1944), 117-149.
28. Plamondon P., Cluster algebras via cluster categories with infinite-dimensional morphism spaces, arXiv:1004.0830.
29. Plamondon P., Cluster characters for cluster categories with infinite-dimensional morphism spaces, arXiv:1002.4956.
30. Ravanini R., Tateo R., Valleriani A., Dynkin TBA's, Internat. J. Modern Phys. A 8 (1993), 1707-1727, hep-th/9207040.
31. Smirnov F.A., Reductions of the sine-Gordon model as a perturbation of minimal models of conformal field theory, Nuclear Phys. B 337 (1990), 156-180.
32. Tateo R., New functional dilogarithm identities and sine-Gordon Y-systems, Phys. Lett. B 355 (1995), 157-164, hep-th/9505022.
33. Zamolodchikov A.B., Integrable field theory from conformal field theory, in Integrable Systems in Quantum Field Theory and Statistical Mechanics, Adv. Stud. Pure Math., Vol. 19, Academic Press, Boston, MA, 1989, 641-674.
34. Zamolodchikov A.B., Thermodynamic Bethe ansatz in relativistic models: scaling 3-state Potts and Lee- Yang models, Nuclear Phys. B 342 (1990), 695-720.
35. Zamolodchikov A.B., Zamolodchikov A.B., Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models, Ann. Physics 120 (1979), 253-291.
36. Zamolodchikov A.B., On the thermodynamic Bethe ansatz equations for reflectionless ADE scattering theories, Phys. Lett. B 253 (1991), 391-394.