Wall crossing, discrete attractor flow and Borcherds algebra

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

Volumn 4, Issue , 2008, Pages

  Cheng, Miranda C N ^a   Verlinde, Erik P ^b  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Black hole; Dyons; Generalized Kac moody algebra

Indexed keywords

EID: 84889234602     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2008.068     Document Type: Article

References (48)

1. Harvey J.A., Moore G.W., Algebras, BPS states, and strings, Nuclear Phys. B 463 (1996), 315-368, hep-th/9510182.
2. Harvey J.A., Moore G.W., On the algebras of BPS states, Comm. Math. Phys. 197 (1998), 489-519, hep-th/9609017.
3. Denef F., Moore G.W., Split states, entropy enigmas, holes and halos, hep-th/0702146.
4. Diaconescu E., Moore G.W., Crossing the wall: branes vs. bundles, arXiv:0706.3193.
5. Kontsevich M., Talk in Paris workshop on Black Holes, Black Rings and Modular Forms 17 (August 2007). Kontsevich M., Soibelman Y., Work in progress.
6. Dijkgraaf R., Verlinde E.P., Verlinde H.L., Counting dyons in N = 4 string theory, Nuclear Phys. B 484 (1997),543-561, hep-th/9607026.
7. Kawai T., N = 2 heterotic string threshold correction, K3 surface and generalized Kac-Moody superalgebra, Phys. Lett. B 372 (1996), 59-64, hep-th/9512046.
8. Gritsenko V., Nikulin V., Siegel automorphic form correction of some Lorentzian Kac-Moody Lie algebras, Amer. J. Math. 119 (1997), 181-224, alg-geom/9504006.
9. Sen A., Walls of marginal stability and dyon spectrum in N = 4 supersymmetric string theories, J. High Energy Phys. 2007 (2007), no. 5, 039, 33 pages, hep-th/0702141.
10. Dabholkar A., Gaiotto D., Nampuri S., Comments on the spectrum of CHL dyons, J. High Energy Phys. 2008 (2008), no. 1, 023, 23 pages, hep-th/0702150.
11. Cheng M.C.N., Verlinde E., Dying dyons don't count, J. High Energy Phys. 2007 (2007), no. 9, 070, 21 pages, arXiv:0706.2363.
12. Sen A., Rare decay modes of quarter BPS dyons, J. High Energy Phys. 2007 (2007), no. 10, 059, 8 pages, arXiv:0707.1563.
13. Dabholkar A., Gomes J., Murthy S., Counting all dyons in N = 4 string theory, arXiv:0803.2692.
14. Sen A., Two centered black holes and N = 4 dyon spectrum, J. High Energy Phys. 2007 (2007), no. 9, 045, 11 pages, arXiv:0705.3874.
15. Sen A., Wall crossing formula for N = 4 dyons: a macroscopic derivation, arXiv:0803.3857.
16. Shih D., Strominger A., Yin X., Recounting dyons in N = 4 string theory, J. High Energy Phys. 2006 (2006), no. 10, 087, 5 pages, hep-th/0505094.
17. David J.R., Sen A., CHL dyons and statistical entropy function from D1-D5 system, J. High Energy Phys. 2006 (2006), no. 11, 072, 40 pages, hep-th/0605210.
18. Cvetic M., Tseytlin A.A., Solitonic strings and BPS saturated dyonic black holes, Phys. Rev. D 53 (1996), 5619-5633, Erratum, Phys. Rev. D 55 (1997), 3907, hep-th/9512031.
19. Cvetic M., Youm D., Dyonic BPS saturated black holes of heterotic string on a six torus, Phys. Rev. D 53 (1996), R584-R588, hep-th/9507090.
20. Damour T., Henneaux M., Nicolai H., Cosmological billiards, Classical Quantum Gravity 20 (2003), R145-R200, hep-th/0212256.
21. Henneaux M., Persson D., Spindel P., Spacelike singularities and hidden symmetries of gravity, Living Rev. Relativity 11 (2008), lrr-2008-1, 232 pages, arXiv:0710.1818.
22. Ferrara S., Kallosh R., Strominger A., N = 2 extremal black holes, Phys. Rev. D 52 (1995), R5412-R5416, hep-th/9508072.
23. Mohaupt T., Black hole entropy, special geometry and strings, Fortsch. Phys. 49 (2001), 3-161, hep-th/0007195.
24. Maldacena J.M., Moore G.W., Strominger A., Counting BPS black holes in toroidal type II string theory, hep-th/9903163.
25. Banerjee S., Sen A., S-duality action on discrete T-duality invariants, J. High Energy Phys. 2008 (2008), no. 4, 012, 8 pages, arXiv:0801.0149.
26. Banerjee S., Sen A., Srivastava Y.K., Generalities of quarter BPS dyon partition function and dyons of torsion two, J. High Energy Phys. 2008 (2008), no. 5, 101, 54 pages, arXiv:0802.0544.
27. Banerjee S., Sen A., Srivastava Y.K., Partition functions of torsion > 1 dyons in heterotic string theory on T6, J. High Energy Phys. 2008 (2008), no. 5, 098, 14 pages, arXiv:0802.1556.
28. Dabholkar A., Harvey J.A., Nonrenormalization of the superstring tension, Phys. Rev. Lett. 63 (1989), 478-481.
29. Dabholkar A., Kallosh R., Maloney A., A stringy cloak for a classical singularity, J. High Energy Phys. 2004 (2004), no. 12, 059, 11 pages, hep-th/0410076.
30. Denef F., Quantum quivers and Hall/hole halos, J. High Energy Phys. 2002 (2002), no. 10, 023, 42 pages, hep-th/0206072.
31. Fré P., Sorin A.S., The arrow of time and the Weyl group: all supergravity billiards are integrable, arXiv:0710.1059.
32. Denef F., Greene B.R., Raugas M., Split attractor flows and the spectrum of BPS D-branes on the quintic, J. High Energy Phys. 2001 (2001), no. 5, 012, 47 pages, hep-th/0101135.
33. Feingold A.J., Frenkel I.B., A hyperbolic Kac-Moody Algebra and the theory of Siegel modular forms of genus 2, Math. Ann. 263 (1983), 87-144.
34. Feingold A.J., Nicolai H., Subalgebras of hyperbolic Kac-Moody algebras, Contemp. Math. 343 (2004), 97-114, math.QA/0303179.
35. Ray U., Automorphic forms and Lie superalgebra, Springer, Dordrecht, 2006.
36. Eguchi T., Ooguri H., Taormina A., Yang S.K., Superconformal algebras and string compactification on manifolds with SU(N) holonomy, Nuclear Phys. B 315 (1989), 193-221.
37. Borcherds R.E., Automorphic forms with singularities on Grassmannian, Invent. Math. 132 (1998), 491-562,alg-geom/9609022.
38. Göttsche L., The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990),193-207.
39. Dijkgraaf R., Moore G.W., Verlinde E.P., Verlinde H.L., Elliptic genera of symmetric products and second quantized strings, Comm. Math. Phys. 185 (1997), 197-209, hep-th/9608096.
40. David J.R., Jatkar D.P., Sen A., Dyon spectrum in generic N = 4 supersymmetric ZN orbifolds, J. High Energy Phys. 2007 (2007), no. 1, 016, 31 pages, hep-th/0609109.
41. Yau S.T., Zaslow E., BPS states, string duality, and nodal curves on K3, Nuclear Phys. B 471 (1996), 503-512, hep-th/9512121.
42. Cachazo F., Fiol B., Intriligator K.A., Katz S., Vafa C., A geometric unification of dualities, Nuclear Phys. B 628 (2002),3-78, hep-th/0110028.
43. Gaiotto D., Re-recounting dyons in N = 4 string theory, hep-th/0506249.
44. Sen A., Three string junction and N = 4 dyon spectrum, J. High Energy Phys. 2007 (2007), no. 12, 019, 12 pages, arXiv:0708.3715.
45. Cheng M.C.N., Dabholkar A., Work in progress.
46. Humphreys J.E., Reflection groups and Coxeter groups, Cambridge University Press, Cambridge, 1990.
47. Björner A., Brenti F., Combinatorics of Coxeter groups, Springer, New York, 2005.
48. Davis M.W., The geometry and topology of Coxeter groups, Princeton University Press, Princeton, NJ, 2008.