Aspects of U-duality in matrix theory

Nuclear Physics B

Volumn 525, Issue 1-2, 1998, Pages 182-214

  Blau, Matthias ^a   O'Loughlin, Martin ^a  

^a ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

D branes; M theory; Matrix theory; U duality

Indexed keywords

EID: 0032504303     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(98)00242-9     Document Type: Article

References (61)

1. [1] C. Hull and P. Townsend, Unity of Superstring dualities, Nucl. Phys. B 438 (1995) 109, hep-th/9410167.
2. d, Nucl. Phys. B 509 (1998) 122, hep-th/9707217.
3. [3] H. Lü, C.N. Pope and K.S. Stelle, Weyl group invariance and p-brane multiplets, Nucl. Phys. B 476 (1996) 89, hep-th/9602140.
4. [4] T. Banks, W. Fischler, S. Shenker and L. Susskind, M-theory as a Matrix model, Phys. Rev. D 55 (1997) 5112, hep-th/9610043.
5. [5] T. Banks, Matrix theory, hep-th/9710231.
6. N and matrix theory, hep-th/9709220.
7. [7] N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577, hep-th/9710009.
8. [8] L. Susskind, Another conjecture about M(atrix) theory, hep-th/9704080.
9. [9] W. Nahm, Monopoles in quantum theory, Proceedings of the Monopole Meeting, Trieste, ed. Craigie et al.; W. Nahm, Self-dual monopoles and calorons, Lecture notes in Physics 201 (Springer, Berlin, 1984); E. Corrigan and P. Goddard, Construction of instanton and monopole solutions and reciprocity, Ann. Phys. 154 (1984) 253; P.J. Braam and P. van Raal, Nahm's transformation for instantons, Nucl. Phys. B 460 (1989) 267.
10. [9] W. Nahm, Monopoles in quantum theory, Proceedings of the Monopole Meeting, Trieste, ed. Craigie et al.; W. Nahm, Self-dual monopoles and calorons, Lecture notes in Physics 201 (Springer, Berlin, 1984); E. Corrigan and P. Goddard, Construction of instanton and monopole solutions and reciprocity, Ann. Phys. 154 (1984) 253; P.J. Braam and P. van Raal, Nahm's transformation for instantons, Nucl. Phys. B 460 (1989) 267.
11. [9] W. Nahm, Monopoles in quantum theory, Proceedings of the Monopole Meeting, Trieste, ed. Craigie et al.; W. Nahm, Self-dual monopoles and calorons, Lecture notes in Physics 201 (Springer, Berlin, 1984); E. Corrigan and P. Goddard, Construction of instanton and monopole solutions and reciprocity, Ann. Phys. 154 (1984) 253; P.J. Braam and P. van Raal, Nahm's transformation for instantons, Nucl. Phys. B 460 (1989) 267.
12. [9] W. Nahm, Monopoles in quantum theory, Proceedings of the Monopole Meeting, Trieste, ed. Craigie et al.; W. Nahm, Self-dual monopoles and calorons, Lecture notes in Physics 201 (Springer, Berlin, 1984); E. Corrigan and P. Goddard, Construction of instanton and monopole solutions and reciprocity, Ann. Phys. 154 (1984) 253; P.J. Braam and P. van Raal, Nahm's transformation for instantons, Nucl. Phys. B 460 (1989) 267.
13. 3, Nucl. Phys. B 508 (1997) 609, hep-th/9707179.
14. [11] J. Harvey and G. Moore, On the algebras of BPS states, hep-th/9609017.
15. [12] A. Connes, M.R. Douglas and A. Schwarz, Non-commutative geometry and Matrix theory: Compactification on tori, hep-th/9711162.
16. [13] M.R. Douglas and C.M. Hull, D-branes and the non-commutative torus, hep-th/9711165.
17. [14] R. Dijkgraaf, E. Verlinde and H. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43, hep-th/9703030; Notes on matrix and micro strings, hep-th/9709107.
18. [15] H. Ooguri and C. Vafa, Summing up D-instantons, Phys. Rev. Lett. 77 (1996) 3296, hep-th/9608079; N. Seiberg and S. Shenker, Hypermultiplet moduli space and string compactification to three-dimensions, Phys. Lett. B 388 (1996) 521, hep-th/9608086.
19. [15] H. Ooguri and C. Vafa, Summing up D-instantons, Phys. Rev. Lett. 77 (1996) 3296, hep-th/9608079; N. Seiberg and S. Shenker, Hypermultiplet moduli space and string compactification to three-dimensions, Phys. Lett. B 388 (1996) 521, hep-th/9608086.
20. [16] C.M. Hull, Matrix Theory, U-duality and toroidal compactification of M-theory, hep-th/9711179.
21. [17] C.M. Hull, U-duality and BPS spectrum of super Yang-Mills theory and M-theory, hep-th/9712075.
22. d with gauge backgrounds, Nucl. Phys. B 525 (1998) 163, preceding article in this issue, hep-th/9712084.
23. 2, Phys. Lett. B 408 (1997) 98, hep-th/9705221.
24. 2, Phys. Lett. B 408 (1997) 98, hep-th/9705221.
25. [20] M. Rozali, Matrix theory and U-duality in seven-dimensions, Phys. Lett. B 400 (1997) 260, hep-th/9702136.
26. [21] D. Berenstein, R. Corrado and J. Distler, On the moduli spaces of M(atrix) theory compactifications, Nucl. Phys. B 503 (19997) 239, hep-th/9704087.
27. [22] W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283, hep-th/9611042.
28. [23] R. Dijkgraaf, E. Verlinde and H. Verlinde, BPS quantization of the five-brane, Nucl. Phys. B 486 (1997) 89, hep-th/9604055.
29. [24] C. Hull and B. Julia, to appear.
30. [25] J. Maldacena, Branes probing black holes, hep-th/9709099.
31. 6, hep-th/9709139.
32. 6, hep-th/9709139.
33. 6, hep-th/9709139.
34. 6, hep-th/9709139.
35. [27] J.H. Schwarz, An SL(2, ℤ) multiplet of type IIB superstrings, hep-th/9508143.
36. [28] E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335, hep-th/9510135.
37. [29] A. Sen, A note on marginally stable bound states in type II string theory, Phys. Rev. D 54 (1996) 2964, hep-th/9510229.
38. [30] J. Polchinski, TASI Lectures on D-branes, hep-th/9611050.
39. [31] O.J. Ganor, S. Ramgoolam, W. Taylor, Branes, fluxes and duality in M(atrix)-theory, Nucl. Phys. B 492 (1997) 191, hep-th/9611202.
40. [32] E. Bergshoeff, M. de Roo, M.B. Green, G. Papadopoulos and P.K. Townsend, Duality of type II 7-branes and 8-branes, Nucl. Phys. B 470 (1996) 113, hep-th/9601150.
41. [33] R.W. Gebert and H. Nicolai, E10 for beginners, hep-th/9411188.
42. [34] S. Ferrara and J. Maldacena, Branes, central charges and U-duality invariant BPS conditions, hep-th/9706097.
43. [35] E. Bergshoeff and M. de Roo, D-branes and T-duality, Phys. Lett. B 380 (1996) 265, hep-th/9603123; M. Green, C. Hull and P. Townsend, D-brane Wess-Zumino actions, T-duality and the cosmological constant, Phys. Lett. B 382 (1996) 65, hep-th/9604119.
44. [35] E. Bergshoeff and M. de Roo, D-branes and T-duality, Phys. Lett. B 380 (1996) 265, hep-th/9603123; M. Green, C. Hull and P. Townsend, D-brane Wess-Zumino actions, T-duality and the cosmological constant, Phys. Lett. B 382 (1996) 65, hep-th/9604119.
45. [36] M. Douglas and G. Moore, D-branes, quivers, and ALE instantons, hep-th/9603167.
46. [37] C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435, hep-th/9512078; Z. Guralnik and S. Ramgoolam, Torons and D-brane bound states, Nucl. Phys. B 499 (1997) 241, hep-th/9702099; Z. Guralnik and S. Ramgoolam, From 0-branes to torons, hep-th/9708089; R. Gopakumar, BPS states in matrix strings, Nucl. Phys. B 507 (1997) 609, hep-th/9704030.
47. [37] C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435, hep-th/9512078; Z. Guralnik and S. Ramgoolam, Torons and D-brane bound states, Nucl. Phys. B 499 (1997) 241, hep-th/9702099; Z. Guralnik and S. Ramgoolam, From 0-branes to torons, hep-th/9708089; R. Gopakumar, BPS states in matrix strings, Nucl. Phys. B 507 (1997) 609, hep-th/9704030.
48. [37] C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435, hep-th/9512078; Z. Guralnik and S. Ramgoolam, Torons and D-brane bound states, Nucl. Phys. B 499 (1997) 241, hep-th/9702099; Z. Guralnik and S. Ramgoolam, From 0-branes to torons, hep-th/9708089; R. Gopakumar, BPS states in matrix strings, Nucl. Phys. B 507 (1997) 609, hep-th/9704030.
49. [37] C. Vafa, Instantons on D-branes, Nucl. Phys. B 463 (1996) 435, hep-th/9512078; Z. Guralnik and S. Ramgoolam, Torons and D-brane bound states, Nucl. Phys. B 499 (1997) 241, hep-th/9702099; Z. Guralnik and S. Ramgoolam, From 0-branes to torons, hep-th/9708089; R. Gopakumar, BPS states in matrix strings, Nucl. Phys. B 507 (1997) 609, hep-th/9704030.
50. [38] G. Moore, Finite in all directions, hep-th/9305139.
51. [39] M. Burkhardt, Light front quantization, Adv. Nucl. Phys, 23 (1996) 1, hep-ph/9505259.
52. [40] S. Hellerman and J. Polchinski, Compactification in the lightlike limit, hep-th/9711037.
53. [41] S. Mukai, Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math. 77 (1984) 101.
54. [42] D. Kutasov and E. Martinec, M-branes and N = 2 strings, Class. Quant. Grav. 34 (1997) 2483, hep-th/9612102.
55. [43] E. Martinec, M-theory and N = 2 strings, hep-th/9710122.
56. [44] R. Kallosh and B. Kol, E(7) symmetric area of the black hole horizon, Phys. Rev. D 53 (1996) 5344, hep-th/9602014; S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Horowitz, J. Maldacena and A. Strominger, Non-extremal black hole microstates and U-duality, Phys. Lett. 383 (1996) 151, hep-th/9603109.
57. [44] R. Kallosh and B. Kol, E(7) symmetric area of the black hole horizon, Phys. Rev. D 53 (1996) 5344, hep-th/9602014; S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Horowitz, J. Maldacena and A. Strominger, Non-extremal black hole microstates and U-duality, Phys. Lett. 383 (1996) 151, hep-th/9603109.
58. [44] R. Kallosh and B. Kol, E(7) symmetric area of the black hole horizon, Phys. Rev. D 53 (1996) 5344, hep-th/9602014; S. Ferrara and R. Kallosh, Universality of supersymmetric attractors, Phys. Rev. D 54 (1996) 1525, hep-th/9603090; G. Horowitz, J. Maldacena and A. Strominger, Non-extremal black hole microstates and U-duality, Phys. Lett. 383 (1996) 151, hep-th/9603109.
59. [45] A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99, hep-th/9601029.
60. [46] J. Maldacena and A. Strominger, Statistical entropy of four-dimensional extremal black holes, Phys. Rev. Lett. 77 (1996) 428, hep-th/9603060.
61. [47] T. Banks and L. Susskind, The number of states of two-dimensional critical string theory, Phys. Rev. D 54 (1996) 1677, hep-th/9511193.