A Hiker's guide to K3. Aspects of N = (4, 4) superconformal field theory with central charge c = 6

Communications in Mathematical Physics

Volumn 216, Issue 1, 2001, Pages 85-136

  Nahm, Werner ^a   Wendland, Katrin ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035530559     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/pl00005548     Document Type: Article

References (67)

1. [A-B-D+] Ademollo, M., Brink, L., D'Adda, A., D'Auria, R., Napolitano, E., Sciuto, S., Del Giudice, E., Di Vecchia, P., Ferrara, S., Gliozzi, F., Musto, R., Pettorino, R.: Supersymmetric strings and color confinement. Phys. Lett. B 62, 105-110 (1976)
2. [A1] Allan, N.: Maximality of some arithmetic groups. Ann. Acad. Brasil. Ci. 38, 223-227 and 243-244 (1966)
3. 2 structure of moduli spaces of Einstein metrics on 4-manifolds. Geom. Funct. Anal. 2, 29-89 (1992)
4. [A-M] Aspinwall, P.S., Morrison, D.R.: String theory on K3 surfaces. In: Greene, B., Yau, S.T. (eds), Mirror symmetry, vol. II, 1994, pp. 703-716; hep-th/9404151
5. [As1] Aspinwall, P.: Enhanced gauge symmetries and K3 surfaces. Phys. Lett. B357, 329-334 (1995); hep-th/9507012
6. [As2] Aspinwall, P.S.: K3 surfaces and string duality. In: Fields, strings and duality (Boulder, CO, 1996). River Edge, NJ: World Sci. Publishing, 1997, pp. 421-540; hep-th/9611137
7. [Be] Berger, M.: Sur les groupes d'holonomie des variétés à connexion affine et des variétés riemmannienes. Bull. Soc. Math. Fr. 83, 279-330 (1955)
8. [B-I] Blum, J.D., Intriligator, K.: Consistency conditions for branes at orbifold singularities. Nucl. Phys. B 506, 223-235 (1997); hep-th/9705030
9. 4/ℤ2 and T-Duality. JHEP 9906:016, (1999); hep-th/9905078
10. [B-T] Budinich, P., Trautmann, A.: The Spinorial Chessboard. Berlin-Heidelberg-New York-London-Paris-Tokyo: Springer-Verlag, 1988
11. [Ce1] Cecotti, S.: N = 2 supergravity, type IIB superstrings and algebraic geometry. Commun. Math. Phys. 131, 517-536 (1990)
12. [Ce2] Cecotti, S.: N = 2 Landau-Ginzburg vs. Calabi-Yau σ-models: Non-perturbative aspects. Int. J. Mod. Phys. A 6, 1749-1813 (1991)
13. [C-E-N-T] Casher, A., Englert, F., Nicolai, H., Taormina, A.: Consistent superstrings as solutions of the D = 26 bosonic string theory. Phys. Lett. B 162, 121-126 (1985)
14. [C-F-G] Cecotti, S., Ferrara, S., Girardello, L.: Geometry of type II superstrings and the moduli of superconformal field theories. Int. J. Mod. Phys. A 4, 2475-2529 (1989)
15. [Cu] Curtright, T.L.: Indices, triality and ultraviolet divergences for supersymmetric theories. Phys. Rev. Lett. 48, 1704-1708 (1982)
16. [D-G] Distler, J., Greene, B.: Some exact results on the superpotential from Calabi-Yau compactifications. Nucl. Phys. B 309, 295-316 (1988)
17. [Di] Dijkgraaf, R.: Instanton strings and hyperkaehler geometry. Nucl. Phys. B 543, 545-571 (1999); hep-th/9810210
18. [D-H-V-W] Dixon, L.J., Harvey, J., Vafa, C., Witten, E.: Strings on orbifolds II. Nucl. Phys. B 274, 285-314 (1986)
19. [Di] Dixon, L.J.: Some world-sheet properties of superstring compactifications, on orbifolds and otherwise. Lectures given at the 1987 ICTP Summer Workshop in High Energy Physics and Cosmology (Trieste, June 29-August 7)
20. [Do] Douglas, M.R.: Enhanced gauge symmetry in M(atrix) theory. JHEP 9707:004 (1997); hep-th/9612126
21. [E-O-T-Y] Eguchi, T., Ooguri, H., Taormina, A., Yang, S.-K.: Superconformal Algebras and String Compactification on Manifolds with SU(n) Holonomy. Nucl. Phys. B 315, 193-221 (1989)
22. [E-T1] Eguchi, T., Taormina, A.: Extended superconformal algebras and string compactifications. Trieste School 1988: Superstrings, pp. 167-188
23. [E-T2] Eguchi, T., Taormina, A.: On the unitary representations of N = 2 and N = 4 superconformal algebras. Phys. Lett. 210, 125-132 (1988)
24. [F-K-S] Fuchs, J., Klemm, A., Schmidt, M.G.: Orbifolds by cyclic permutations in Gepner type superstrings and in the corresponding Calabi-Yau manifolds. Ann. Phys. 214, 221-257 (1992)
25. [F-K-S-S] Fuchs, J., Klemm, A., Scheich, Ch., Schmidt, M.G.: Spectra and symmetries of Gepner models compared to Calabi-Yau compactifications. Ann. Phys. 204, 1-51 (1990)
26. [Ge1] Gepner, D.: Exactly solvable string compactifications on manifolds of SU (N) holonomy. Phys. Lett. B 199, 380-388 (1987)
27. [Ge2] Gepner, D.: Space-time supersymmetry in compactified string theory and superconformal models. Nucl. Phys. B 296, 757-778 (1988)
28. [G-O] Goddard, P., Olive, D.: Kac-Moody and Virasoro algebras in relation to quantum physics. Int. J. Mod. Phys. A 2, 303-414 (1986)
29. [G-P] Greene, B.R., Plesser, M.R.: Duality in Calabi-Yau moduli space. Nucl. Phys. B 338, 15-37 (1990)
30. [G-V-W] Greene, B.R., Vafa, C., Warner, N.: Calabi-Yau manifolds and renormalization group flows. Nucl. Phys. B 324, 371-390 (1989)
31. [H-V] Hamidi, S., Vafa, C.: Interactions on orbifolds. Nucl. Phys. B 279, 465-513 (1987)
32. 3. J. Fac. Sci. Univ. Tokyo Sec. IA 23, 545-560 (1976)
33. [Ko] Kodaira, K.: On the structure of compact complex analytic surfaces. I. Am. J. Math. 86, 751-798 (1964)
34. [K-O-P] Kiritsis, E., Obers, N., Pioline, B.: Heterotic/type II triality and instantons on K (3). JHEP 0001:029, (2000); hep-th/0001083
35. [K-S] Kobayashi, K.-I., Sakamoto, M.: Orbifold-compactified models in torus-compactified string theories. Z. Phys. C 41, 55-63 (1988)
36. [K-T] Kobayashi, R., Todorov, A.N.: Polarized period map for generalized K3 surfaces and the moduli of Einstein metrics. Tôhoku Math. J. 39, 341-363 (1987)
37. [L-M] Lawson, H.B., Michelsohn, M.-L.: Spin Geometry. Princeton, NJ: Princeton University Press, 1989
38. [L-P] Looijenga, E., Peters, C.: Torelli theorems for K3-surfaces. Compos. Math. 42, 145-186 (1981)
39. [L-V-W] Lerche, W., Vafa, C., Warner, N.P.: Chiral rings in N = 2 superconformal theories. Nucl. Phys. B 324, 427-474 (1989)
40. [Mu] Mukai, S.: Finite groups of automorphisms of K3 surfaces and the Mathieu group. Invent. Math. 94, 183-221 (1988)
41. [Na] Narain, K.S.: New heterotic string theories in uncompactified dimensions < 10. Phys. Lett. B 169, 41-46 (1986)
42. [Ni1] Nikulin, V.V.: On Kummer Surfaces. Math. USSR Isv. 9, 261-275 (1975)
43. [Ni2] Nikulin, V.V.: Finite automorphism groups of Kaehler K3 surfaces. Trans. Mosc. Math. Soc. 38, 71-135 (1980)
44. [Ni3] Nikulin, V.V.: Integral symmetric bilinear forms and some of their applications. Math. USSR Isv. 14, 103-167 (1980)
45. [N-S] Nagura, M., Sugiyama, K.: Mirror symmetry of K3 and torus. Int. J. Mod. Phys. A 10, 233-252 (1995); hep-th/9312159
46. [O-P1] Obers, N., Pioline, B.: Eisenstein series and string thresholds. Commun. Math. Phys. 209, 275-324 (2000); hep-th/9903113
47. [O-P2] Obers, N., Pioline, B.: Eisenstein series in string theory. Classical Quantum Gravity 17, 1215-1224 (2000); hep-th/9910115
48. [P-S] Periwal, V., Strominger, A.: Kahler geometry of the space of N = 2 superconformal field theories. Phys. Lett. B 235, 261-267 (1990)
49. [Qi] Qiu, Z.: Modular invariant partition functions for N = 2 superconformal field theories. Phys. Lett. B 198, 497-502 (1987)
50. [R-W] Ramgoolam, S., Waldram, D.: Zero branes on a compact orbifold. JHEP 9807:009 (1998): hep-th/9805191
51. [R-Y] Ravanini, F., Yang, S.-K.: Modular invariance in N = 2 superconformal field theories. Phys. Lett. B 195, 202-208 (1987)
52. [Sei] Seiberg, N.: Observations on the moduli space of superconformal field theories. Nucl. Phys. B 303, 286-304 (1988)
53. [Se1] Sen, A.: (2,0) supersymmetry and space-time supersymmetry in the heterotic string theory. Nucl. Phys. B 278, 289-308 (1986)
54. [Se2] Sen, A.: Heterotic string theory on Calabi-Yau manifolds in the Green-Schwarz formalism. Nucl. Phys. B 284, 423-448 (1987)
55. [Sha] Shankar, R.: Some novel features of the Gross-Neveu model. Phys. Lett. 92B, 333-336 (1980)
56. [Shi] Shioda, T., Inose, H.: On singular K3 surfaces. In: Bailey, W.L., Shioda, T. (eds), Complex Analysis and Algebraic Geometry. Cambridge: Cambridge Univ. Press, 1977, pp. 119-136
57. [Si] Simons, J.: On transitivity on holonomy systems. Ann. Math. 76, 213-234 (1962)
58. [S-W1] Schellekens, A., Warner, N.: Anomalies and modular invariance in string theory. Phys. Lett. B 177, 317-323 (1986)
59. [S-W2] Schellekens, A., Warner, N.: Anomaly cancellation and selfdual lattices. Phys. Lett. B 181, 339-343 (1986)
60. [Ta] Taormina, A.: The N = 2 and N = 4 superconformal algebras and string compactifications. Islamabad 1989, Proc. Mathematical Physics.
61. [Wa] Walton, M.: The Heterotic string on the simplest Calabi-Yau manifold and its orbifold limits. Phys. Rev. D 37, 377-390 (1988)
62. [We] Wendland, K.: Consistency of orbifold conformal field theories on K3. hep-th/0010281
63. [Wi 1] Witten, E.: Elliptic genera and quantum field theory. Commun. Math. Phys. 109, 525-536 (1987)
64. [Wi2] Witten, E.: The index of the Dirac operator in loop space. In: Landweber, P. (ed), Elliptic curves and modular forms in algebraic geometry. Berlin-Heidelberg-New York: Springer-Verlag, 1988, pp. 161-181
65. [Wi3] Witten, E.: String theory dynamics in various dimensions. Nucl. Phys. B 443, 85-126 (1995); hep-th/9503124
66. [Wo] Wolf, J.A.: Complex homogeneous contact manifolds and quaternionic symmetric spaces. J. Math. Mech. 14, 1033-1047 (1965)
67. [Za] Zamolodchikov, A.B.: "Irreversibility" of the flux of the renormalization group in a 2-D field theory. JETP Lett. 43, 730-732 (1986)