On the Complete Classification of Unitary N = 2 Minimal Superconformal Field Theories

Communications in Mathematical Physics

Volumn 312, Issue 3, 2012, Pages 611-654

  Gray, Oliver ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

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EID: 84861645100     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-012-1478-z     Document Type: Article

References (75)

1. Adamovic D.: Vertex algebra approach to fusion rules for N = 2 superconformal minimal models. J. Algebra 239(2), 549-572 (2001).
2. Ademollo M. et al.: Supersymmetric strings and color confinement. Phys. Lett. B62, 105 (1976).
3. Becker K., Becker M., Schwarz J. H.: String theory and M-theory: A modern introduction. Cambridge University Press, Cambridge (2007).
4. Belavin A. A., Polyakov A. M., Zamolodchikov A. B.: Infinite conformal symmetry in two-dimensional quantum field theory. Nucl. Phys. B241, 333-380 (1984).
5. Boucher W., Friedan D., Kent A.: Determinant formulae and unitarity for the N = 2 superconformal algebras in two-dimensions or exact results on string compactification. Phys. Lett. B172, 316 (1986).
6. Buscher T. H.: A Symmetry of the String Background Field Equations. Phys. Lett. B194, 59 (1987).
7. Cappelli A., Itzykson C., Zuber J. B.: The ADE classification of minimal and A-B-C conformal invariant theories. Commun. Math. Phys. 113, 1-39 (1987).
8. Cardy, J.: Conformal field theory and statistical mechanics. In Exact methods in low-dimensional statistical physics and quantum computing. Volume LXXXIX of Les Houche summer session, Jun 2008. Available at http://arxiv. org/abs/0807. 3472v1 [cmd-mat. stat. mech], 2008.
9. Cecotti S., Vafa C.: On classification of N = 2 supersymmetric theories. Commun. Math. Phys. 158, 569-644 (1993).
10. Coste A., Gannon T.: Remarks on Galois symmetry in rational conformal field theories. Phys. Lett. B323, 316-321 (1994).
11. Di Francesco P., Mathieu P., Senechal D.: Conformal field theory. Springer-Verlag, Berlin Heidelberg-Newyork (1997).
12. Di Vecchia P., Petersen J. L., Yu M.: On the unitary representations of N = 2 superconformal theory. Phys. Lett. B172, 211 (1986).
13. Di Vecchia P., Petersen J. L., Yu M., Zheng H. B.: Explicit construction of unitary representations of the N = 2 superconformal algebra. Phys. Lett. B174, 280 (1986).
14. Dixon L. J., Harvey J. A., Vafa C., Witten E.: Strings on orbifolds. Nucl. Phys. B261, 678-686 (1985).
15. Dixon L. J., Harvey J. A., Vafa C., Witten E.: Strings on orbifolds. 2. Nucl. Phys. B274, 285-314 (1986).
16. Dobrev V. K.: Characters of the unitarizable highest weight modules over the N = 2 superconformal algebras. Phys. Lett. B186, 43 (1987).
17. Dobrev, V. K.: Characters of the unitarizable highest weight modules over the N = 2 superconformal algebras. http://arxiv. org/abs/0708. 1719v1 [hepth], 2007.
18. Dörrzapf M.: The embedding structure of unitary N = 2 minimal models. Nucl. Phys. B529, 639-655 (1998).
19. Eholzer W., Gaberdiel M. R.: Unitarity of rational N = 2 superconformal theories. Commun. Math. Phys. 186, 61-85 (1997).
20. Feigin, B. L., Semikhatov, A. M.: Free-field resolutions of the unitary N = 2 super-Virasoro representations. http://arxiv. org/abs/hepth/9810059v1, 1998.
21. Friedan D., Qiu Z., Shenker S. H.: Superconformal invariance in two-dimensions and the tricritical Ising model. Phys. Lett. B151, 37-43 (1985).
22. Fröhlich, J., Fuchs, J., Runkel, I., Schweigert, C.: Defect lines, dualities, and generalised orbifolds. In: Proceedings of the XVI International Congress on Mathematical Physics, Hackensack, NJ: world scientific pub., pp. 608-613.
23. Fuchs J., Runkel I., Schweigert C.: TFT construction of RCFT correlators I: Partition functions. Nucl. Phys. B646, 353-497 (2002).
24. Gaberdiel M. R.: An introduction to conformal field theory. Rept. Prog. Phys. 63, 607-667 (2000).
25. Gaberdiel M. R., Goddard P.: Axiomatic conformal field theory. Commun. Math. Phys. 209, 549-594 (2000).
26. Gannon, T.: Kac-Peterson, Perron-Frobenius, and the classification of conformal field theories, 1995, http://arxiv. org/abs/q-alg/9510026v1, 1995.
27. Gannon T.: Towards a classification of SU(2) x SU(2) modular invariant partition functions. J. Math. Phys. 36, 675-706 (1995).
28. Gannon T.: The classification of SU(3) modular invariants revisited. Ann. Poincare 65, 15-56 (1996).
29. m modular invariants, N = 2 minimal models, and the quantum Hall effect. Nucl. Phys. B491, 659-688 (1997).
30. Gannon T.: Boundary conformal field theory and fusion ring representations. Nucl. Phys. B627, 506-564 (2002).
31. Gannon T., Walton M. A.: On the classification of diagonal coset modular invariants. Commun. Math. Phys. 173, 175-198 (1995).
32. k. Commun. Math. Phys. 145, 85-122 (1992).
33. Gepner D.: On the spectrum of 2D conformal field theories. Nucl. Phys. B287, 111 (1987).
34. Gepner D.: Space-time supersymmetry in compactified string theory and superconformal models. Nucl. Phys. B296, 757 (1988).
35. Gepner D., Witten E.: String theory on group manifolds. Nucl. Phys. B278, 493 (1986).
36. Ginsparg, P. H.: Applied conformal field theory. In: Strings, fields and critical phenomena, Volume XLIX of Les Houche summer session, June 1988, http://arxiv. org/abs/hepth/9108028v1, 1991.
37. Goddard P., Kent A., Olive D. I.: Virasoro algebras and coset space models. Phys. Lett. B152, 88 (1985).
38. Gray, O.: On the complete classification of unitary N = 2 minimal superconformal field theories. PhD thesis, Universität Augsburg, 2009.
39. Green, M. B., Schwarz, J. H., Witten, E.: Superstring theory. Vol. 1: Introduction. Cambridge: Cambridge Univ. Press, 1987.
40. Green, M. B., Schwarz, J. H., Witten, E.: Superstring theory. Vol. 2: Loop amplitudes, anomalies and phenomenology. Cambridge: Cambridge Univ. Press, 1987.
41. Greene, B. R.: String theory on Calabi-Yau manifolds. 1996, http://arxiv. org/abs/hepth/970455v1, 1997.
42. Intriligator K. A.: Bonus symmetry in conformal field theory. Nucl. Phys. B332, 541 (1990).
43. Kac V. G., Peterson D. H.: Infinite-dimensional Lie algebras, theta functions and modular forms. Adv. Math. 53, 125-264 (1984).
44. Kiritsis E. B.: The structure of N = 2 superconformally invariant 'minimal' theories: Operator algebra and correlation functions. Phys. Rev. D36, 3048 (1987).
45. Kiritsis E. B.: Character formulae and the structure of the representations of the N = 1, N = 2 superconformal algebras. Int. J. Mod. Phys. A3, 1871 (1988).
46. Knizhnik V. G., Zamolodchikov A. B.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys. B247, 83-103 (1984).
47. Kreuzer M., Schellekens A. N.: Simple currents versus orbifolds with discrete torsion: A complete classification. Nucl. Phys. B411, 97-121 (1994).
48. Longo R., Rehren K.-H.: Nets of subfactors. Rev. Math. Phys. 7, 567-598 (1995).
49. Martinec E. J.: Algebraic geometry and effective Lagrangians. Phys. Lett. B217, 431 (1989).
50. Matsuo Y.: Character formula of c & 1 unitary representation of N = 2 superconformal algebra. Prog. Theor. Phys. 77, 793 (1987).
51. Moore G. W., Seiberg N.: Polynomial equations for rational conformal field theories. Phys. Lett. B212, 451 (1988).
52. Moore G. W., Seiberg N.: Naturality in conformal field theory. Nucl. Phys. B313, 16 (1989).
53. Mussardo G., Sotkov G., Stanishkov M.: Fusion rules, four point functions and discrete symmetries of N = 2 superconformal models. Phys. Lett. B218, 191 (1989).
54. Mussardo G., Sotkov G., Stanishkov M.: N = 2 superconformal minimal models. Int. J. Mod. Phys. A4, 1135 (1989).
55. Onsager L.: Crystal statistics. 1. A two-dimensional model with an order disorder transition. Phys. Rev. 65, 117-149 (1944).
56. Polchinski, J.: String Theory, Volume I: An Introduction to the Bosonic String. Cambridge: Cambridge Univ. Press, 2005.
57. Qiu Z.: Modular invariant partition functions for N = 2 superconformal field theories. Phys. Lett. B198, 497 (1987).
58. Qiu Z.: Nonlocal current algebra and N = 2 superconformal field theory in two-dimensions. Phys. Lett. B188, 207 (1987).
59. Ravanini F., Yang S.: Modular invariance in N = 2 superconformal field theories. Phys. Lett. B195, 202 (1987).
60. Rocek M., Verlinde E. P.: Duality, quotients, and currents. Nucl. Phys. B373, 630-646 (1992).
61. Schellekens A. N., Yankielowicz S.: Extended chiral algebras and modular invariant partition functions. Nucl. Phys. B327, 673 (1989).
62. Schellekens A. N., Yankielowicz S.: Modular invariants from simple currents: An explicit proof. Phys. Lett. B227, 387 (1989).
63. Sonoda H.: Sewing conformal field theories 2. Nucl. Phys. B311, 417 (1988).
64. Turaev V. G.: Quantum invariants of knots and three manifolds. De Gruyter Stud. Math. 18, 1-588 (1994).
65. Vafa C.: Modular invariance and discrete torsion on orbifolds. Nucl. Phys. B273, 592 (1986).
66. Vafa C., Warner N. P.: Catastrophes and the classification of conformal theories. Phys. Lett. B218, 51 (1989).
67. Verlinde E. P.: Fusion rules and modular transformations in 2D conformal field theory. Nucl. Phys. B300, 360 (1988).
68. Wakimoto, M.: Fusion rules for N = 2 superconformal modules, 1998, http://arxiv. org/abs/hepth/9807144v2, 1998.
69. Waterson G.: Bosonic construction of an N = 2 extended superconformal theory in two-dimensions. Phys. Lett. B171, 77 (1986).
70. Wess J., Zumino B.: Consequences of anomalous Ward identities. Phys. Lett. B37, 95 (1971).
71. Witten E.: Nonabelian bosonization in two dimensions. Commun. Math. Phys. 92, 455-472 (1984).
72. Yu M., Zheng H. B.: N = 2 superconformal invariance in two-dimensional quantum field theories. Nucl. Phys. B288, 275 (1987).
73. Zamolodchikov A. B., Fateev V. A.: Disorder fields in two-dimensional conformal quantum field theory and N = 2 extended supersymmetry. Sov. Phys. JETP 63, 913-919 (1986).
74. Zamolodchikov A. B., Fateev V. A.: Operator algebra and correlation functions in the two-dimensional Wess-Zumino SU(2) × SU(2) chiral model. Sov. J. Nucl. Phys. 43, 657-664 (1986).
75. Zuber, J.-B.: CFT, BCFT, ADE and all that. In: Quantum symmetries in theoretical physics and mathematics, Jan 2000, http://arxiv. org/abs/hepth/0006151v1, 2000.