Conformal field theory and torsion elements of the bloch group

Frontiers in Number Theory, Physics, and Geometry II: On Conformal Field Theories, Discrete Groups and Renormalization

Volumn , Issue , 2007, Pages 67-132

  Nahm, Werner ^a,b  

^a DUBLIN INSTITUTE FOR ADVANCED STUDIES   (Ireland)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

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EID: 84895293248     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-540-30308-4_2     Document Type: Chapter

References (35)

1. E. Ardonne, P. Bouwknegt, and P. Dawson, K-matrices for 2D conformal field theories, Nucl.Phys. B660 (2003), 473-531
2. G.E. Andrews, The theory of partitions, in: Encyclopedia of Mathematics and its Applications, Vol. 2, Addison Wesley, 1976
3. A. Berkovich, B.M. McCoy, The universal chiral partition function for exclusion statistics, hep-th/9808013
4. P. Dorey, Exact S-matrices, hep-th/9810026
5. A. Coste, T. Gannon, Remarks on Galois symmetry in rational conformal field theories, Phys.Lett. B323 (1994), 316-321
6. P. Dorey, R. Tateo, Excited states in some simple perturbed conformal field theories, Nucl.Phys. B515 (1998), 575-623
7. E. Frenkel, A. Szenes, Crystal bases, dilogarithm identities and torsion in algebraic K-groups, J. Amer. Math. Soc. 8 (1995), 629-664, hep-th/9304118
8. E. Frenkel, A. Szenes, Thermodynamic Bethe Ansatz and Dilogarithm Identities I, Math. Res. Lett. 2 (1995), 677-693, hep-th/9506215
9. H. Gangl, D. Zagier, Classical and Elliptic Polylogarithms and Special Values of L-Series, in: B.B. Gordon et al. eds., The Arithmetic and Geometry of Algebraic Cycles, 2000
10. F. Gliozzi, R. Tateo, Thermodynamic Bethe Ansatz and Threefold Triangulations, Int.J.Mod.Phys. A11 (1996), 4051-4064
11. F. Gliozzi, R. Tateo, ADE functional dilogarithm identities and integrable models, Phys.Lett. B348 (1995), 84-88
12. R. Hirota, Discrete analogue of a generalized Toda equation, J.Phys. Soc. Jpn. 50 (1981) 3785-3791
13. 2 Phys.Lett. B304 (1993), 263-270
14. A.N. Kirillov, Identities for the Rogers Dilogarithm Function Connected with Simple Lie Algebras, J. Soviet Mathematics 47 (1989), 2450-2459
15. A.N. Kirillov, N.Yu. Reshetikhin, Representations of Yan-gians and Multiplicities of Occurrence of the Irreducible Components of the Tensor Product of Representations of Simple Lie Algebras, J. Soviet Mathematics 52 (1990), 3156-3164
16. T. Klassen, E. Melzer, Purely Elastic Scattering Theories And Their Ultraviolet Limits, Nucl.Phys. B338 (1990), 485-528
17. A. Kuniba, T. Nakanishi, Spectra in Conformal Field Theories from the Rogers Dilogarithm, Mod.Phys.Lett. A7 (1992), 3487-3494
18. A. Kuniba, T. Nakanishi, J. Suzuki, Characters in Con-formal Field Theories from Thermodynamic Bethe Ansatz, Mod.Phys.Lett. A8 (1993), 1649-1660
19. M. Lässig, M.J. Martins, Finite-Size Effects in Theories with Factorizable S-Matrices, Nucl.Phys. B354 (1991), 666-688
20. T. Miwa, On Hirota's difference equations, Proc. Japan Acad. A58 (1982) 9-12.
21. M.J. Martins, Complex Excitations in the Thermodynamic Bethe Ansatz, Phys.Rev.Lett. 67 (1991), 419-421
22. W. Nahm, Conformal Field Theory, Dilogarithms, and Three Dimensional Manifolds, in: Interface between physics and mathematics, Proceedings, Hangzhou 1993, W. Nahm and J.M. Shen eds., World Scientific
23. W. Nahm, A. Recknagel, and M. Terhoeven, Dilogarithm Identities in Conformal Field Theory, Mod.Phys.Lett. A8 (1993), 1835-1848
24. W.D. Neumann, Extended Bloch Group and the Cheeger-Chern-Simons Class, math.GT/0307092
25. W.D. Neumann, D. Zagier, Volumes of hyperbolic 3-manifolds, Topology 24 (1985), 307-332
26. A. Ocneanu, Paths on Coxeter Diagrams: From Platonic Solids and Singularities to Minimal Models and Subfactors, AMS Fields Institute Monographs no. 13, (1999), B.V. Rajarama Bhat, G, A, Elliott, P.A. Fillmore eds., vol. 'Lectures on Operator Theory'
27. V. Kac, Infinite Dimensional Lie Algebras, Third edition, Cambridge University Press, Cambridge 1990
28. A.A. Suslin, Algebraic K-theory of fields, ICM, Berkeley, I (1986) 222-244
29. C.H. Sah, Homology of Classical Lie Groups made Discrete, III, J. Pure Appl. Algebra 56 (1989) 313-318
30. 7 Rogers-Ramanujan identities J.Phys. A27 (1994) L891-L898.
31. S. Weinzierl, Algebraic Algorithms in Perturbative Calculations, hep-th/0305260, this volume
32. D. Zagier, Polylogarithms, Dedekind zeta functions and the algebraic K-theory of fields, in: Progr. Math. 89 (1991), Birkḧauser Boston, Boston MA, 391-430
33. A.B. Zamolodchikov, Integrable field theory from conformal field theory, Adv. Stud. in Pure Math. 19 (1989), 641
34. A.B. Zamolodchikov, On The Thermodynamic Bethe Ansatz Equations For Reflectionless Ade Scattering Theories, Phys.Lett. B253 (1991), 391-394.
35. D. Zagier, The Dilogarithm Function, this volume