Borcherds symmetries in M-theory

Journal of High Energy Physics

Volumn 6, Issue 4, 2002, Pages 1181-1211

  Henry Labordère, Pierre ^a   Julia, Bernard ^b   Paulot, Louis ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

Differential and algebraic geometry; Global symmetries; M theory; String duality

Indexed keywords

EID: 23044490101     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2002/04/049     Document Type: Article

References (35)

1. A. Iqbal, A. Neitzke and C. Vafa, A mysterious duality, hep-th/0111068.
2. R. Slansky, An algebraic role for energy and number operators for multiparticle states, Nucl. Phys. B 389 (1993) 349.
3. E. Cremmer, B. Julia, H. Lü and C.N. Pope, Dualisation of dualities, 2. Twisted self-duality of doubled fields and super dualities, Nucl. Phys. B 535 (1998) 242 [hep-th/9806106].
4. B.L. Julia, Dualities in the classical supergravity limits: dualisations, dualities and a detour via 4k + 2 dimensions, hep-th/9805083.
5. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York 1977.
6. P. Griffiths and J. Harris, Principles of algebraic geometry, John Wiley and Sons Inc., New York, 1994, reprint of the 1978 original.
7. Y. Nakai, Some fundamental lemmas on projective schemes, Trans. Amer. Math. Soc. 109 (1963) 296.
8. O. Debarre, Higher-dimensional algebraic geometry, Universitext, Springer 2001.
9. R.E. Borcherds, Generalized Kac-Moody algebras, J. of Alg. 115 No. 2 (1988).
10. U. Ray, A character formula for generalized Kac-Moody algebras, J. of Alg. 177 (1995) 154.
11. V.A. Gritsenko and V.V. Nikulin, K3 surfaces, lorentzian Kac-Moody algebras and mirror symmetry, alg-geom/9510008.
12. Yu.I. Manin, Cubic forms: algebra, geometry, arithmetic, North-Holland, Amsterdam 1974.
13. Yu.I. Manin, private communication.
14. E. Cremmer, B. Julia and J. Scherk, Supergravity theory in 11 dimensions, Phys. Lett. B 76 (1978) 409.
15. I.V. Lavrinenko, H. Lü, C.N. Pope and K.S. Stelle, Superdualities, brane tensions and massive IIA/IIB duality, Nucl. Phys. B 555 (1999) 201 [hep-th/9903057].
16. B. Julia, Superdualities: below and beyond U-duality, hep-th/0002035;
17. Magics of M-gravity, Fortschr. Phys. 49 (2001) 551 [hep-th/0105031];
18. Supergravities: from fields to branes, hep-th/0107009.
19. R.E. Borcherds, The monster Lie algebra, Adv. Math. 8 (1990) 30.
20. J.A. Minahan, D. Nemeschansky, C. Vafa and N.P. Warner, E-strings and N = 4 topological Yang-Milk theories, Nucl. Phys. B 527 (1998) 581 [hep-th/9802168].
21. P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction I, II, III, Proc. Cambridge Phil. Soc. 30 (1934) 453;
22. Proc. Cambridge Phil. Soc. 30 (1934) 483.
23. M. Demazure, Surfaces de del Pezzo, Séminaire sur les Singularités des Surfaces, Lecture Notes in Mathematics 777, Springer 1980.
24. F. Hidaka and K. Watanabe, Normal Gorenstein surfaces with ample anti-canonical divisor, Tokyo J. Math. 4 No. 2 (1981) 319.
25. M. Reid, Nonnormal del Pezzo surfaces, alg-geom/9404002.
26. M. Reid, Chapters on algebraic surfaces, alg-geom/9602006.
27. E. Cremmer, B. Julia, H. Lü and C.N. Pope, Higher-dimensional origin of D = 3 coset symmetries, hep-th/9909099.
28. M. Miyanishi and D.-Q. Zhang, Gorenstein log del Pezzo surfaces of rank one, J. of Alg. 118 (1988) 63.
29. M. Miyanishi and D.-Q. Zhang, Gorenstein log del Pezzo surfaces, 2, J. of Alg. 156 (1993) 183.
30. Q. Ye, On Gorenstein log del Pezzo surfaces, math. AG/0109223.
31. J.A. Harvey and G.W. Moore, Algebras, BPS states and strings, Nucl. Phys. B 463 (1996) 315 [hep-th/9510182].
32. J.A. Harvey and G.W. Moore, Exact gravitational threshold correction in the fhsv model, Phys. Rev. D 57 (1998) 2329 [hep-th/9611176].
33. R. Dijkgraaf, E. Verlinde and H. Verlinde, Counting dyons in N = 4 string theory, Nucl. Phys. B 484 (1997) 543 [hep-th/9607026].
34. T. Kawai, n = 2 heterotic string threshold correction, K3 surface and generalized Kac-Moody superalgebra, Phys. Lett. B 372 (1996) 59 [hep-th/9512046].
35. R.E. Borcherds, Automorphic forms with singularities on Grassmannians, Invent. Math. 132 (1998) 491 [alg-geom/9609022].