Monopole dynamics in script N = 2 super Yang-Mills theory from a threebrane probe

Nuclear Physics B

Volumn 559, Issue 1-2, 1999, Pages 143-164

  De Mello Koch, Robert ^a   Paulin Campbell, Alastair ^b   Rodrigues, João P ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF THE WITWATERSRAND   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033581534     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(99)00422-8     Document Type: Article

References (80)

1. [1] A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230; E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3, hep-th/9703166.
2. [1] A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152, hep-th/9611230;
3. [2] S. Gukov, Seiberg-Witten solution from Matrix theory, hep-th/9709138; A. Kapustin, Solution of N = 2 gauge theories via compactification to three dimensions, Nucl. Phys. B534 (1998) 531, hep-th/9804069; R. De Mello Koch and J.P. Rodrigues, Solving four-dimensional field theories with the Dirichlet fivebrane,to appear in Phys. Rev. D, hep-th/9811036.
4. [2] S. Gukov, Seiberg-Witten solution from Matrix theory, hep-th/9709138; A. Kapustin, Solution of N = 2 gauge theories via compactification to three dimensions, Nucl. Phys. B 534 (1998) 531, hep-th/9804069; R. De Mello Koch and J.P. Rodrigues, Solving four-dimensional field theories with the Dirichlet fivebrane,to appear in Phys. Rev. D, hep-th/9811036.
5. [2] S. Gukov, Seiberg-Witten solution from Matrix theory, hep-th/9709138; A. Kapustin, Solution of N = 2 gauge theories via compactification to three dimensions, Nucl. Phys. B534 (1998) 531, hep-th/9804069; R. De Mello Koch and J.P. Rodrigues, Solving four-dimensional field theories with the Dirichlet fivebrane, to appear in Phys. Rev. D, hep-th/9811036.
6. [3] N.D. Lambert and P.C. West, N = 2 superfields and the M-fivebrane, Phys. Lett. B 424 (1998) 281, hep-th/9801104; N.D. Lambert and P.C. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141,hep-th/9712040; P.S. Howe, N.D. Lambert and P.C. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th 9710034; J. De Boer, K. Hori, H. Ooguri and Y. Oz, Kähler potential and higher derivative terms from M-theory fivebrane, Nucl. Phys. B 518 (1998) 173, hep-th/9711143.
7. [3] N.D. Lambert and P.C. West, N = 2 superfields and the M-fivebrane, Phys. Lett. B 424 (1998) 281,hep-th/9801104; N.D. Lambert and P.C. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141, hep-th/9712040; P.S. Howe, N.D. Lambert and P.C. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th 9710034; J. De Boer, K. Hori, H. Ooguri and Y. Oz, Kähler potential and higher derivative terms from M-theory fivebrane, Nucl. Phys. B 518 (1998) 173, hep-th/9711143.
8. [3] N.D. Lambert and P.C. West, N = 2 superfields and the M-fivebrane, Phys. Lett. B 424 (1998) 281,hep-th/9801104; N.D. Lambert and P.C. West, Gauge fields and M-fivebrane dynamics, Nucl. Phys. B 524 (1998) 141,hep-th/9712040; P.S. Howe, N.D. Lambert and P.C. West, Classical M-fivebrane dynamics and quantum N = 2 Yang-Mills, Phys. Lett. B 418 (1998) 85, hep-th 9710034; J. De Boer, K. Hori, H. Ooguri and Y. Oz, Kähler potential and higher derivative terms from M-theory fivebrane, Nucl. Phys. B 518 (1998) 173, hep-th/9711143.
9. J. De Boer, K. Hori, H. Ooguri and Y. Oz, Kähler potential and higher derivative terms from M-theory fivebrane, Nucl. Phys. B 518 (1998) 173, hep-th/9711143.
10. [4] E. Witten, Branes and the dynamics of QCD, Nucl. Phys. B 507 (1997) 658, hep-th/9706109; H. Ooguri, M-theory fivebrane and SQCD, Nucl. Phys. B (Proc. Suppl.) 68 (1998) 84, hep-th/9709211.
11. [4] E. Witten, Branes and the dynamics of QCD, Nucl. Phys. B 507 (1997) 658, hep-th/9706109; H. Ooguri, M-theory fivebrane and SQCD, Nucl. Phys. B (Proc. Suppl.) 68 (1998) 84, hep-th/9709211.
12. [5] A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562, hep-th/9605150; T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 74,hep-th/9605199; M.R. Douglas, D.A. Lowe and J.H. Schwarz, Probing F-theory with multiple branes, Phys. Lett. B 394(1997) 297, hep-th/9612062.
13. [5] A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562, hep-th/9605150; T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 74, hep-th/9605199; M.R. Douglas, D.A. Lowe and J.H. Schwarz, Probing F-theory with multiple branes, Phys. Lett. B 394(1997) 297, hep-th/9612062.
14. [5] A. Sen, F-theory and orientifolds, Nucl. Phys. B 475 (1996) 562, hep-th/9605150; T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 74,hep-th/9605199; M.R. Douglas, D.A. Lowe and J.H. Schwarz, Probing F-theory with multiple branes, Phys. Lett. B 394 (1997) 297, hep-th/9612062.
15. [6] O. Aharony, A. Fayyazuddin and J. Maldacena, The large-N limit of N = 2, 1 field theories from threebranes in F-theory, JHEP 9807 (1998) 013, hep-th/9806159.
16. [7] R. De Mello Koch and R. Tatar, Higher derivative terms from threebranes in F-theory, Phys. Lett. B 450 (1999) 99, hep-th/9811128.
17. [8] R. De Mello Koch, A. Paulin-Campbell and J.P. Rodrigues, Non-holomorphic corrections from threebranes in F-theory, hep-th/9903029.
18. [9] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 super-Yang-Mills theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087; N. Seiberg and E. Witten, Monopoles, Duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
19. [9] N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation and confinement in N = 2 super-Yang-Mills theory, Nucl. Phys. B 426 (1994) 19, hep-th/9407087; N. Seiberg and E. Witten, Monopoles, Duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484, hep-th/9408099.
20. [10] F. Ferrari, The dyon spectra of finite gauge theories, Nucl. Phys. B 501 (1997) 53, hep-th/9702166.
21. [11] A. Sen, BPS states on a threebrane probe, hep-th/9608005.
22. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995) 2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
23. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Mills theories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
24. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl. Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
25. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469 (1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
26. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetric field theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
27. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2 supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gaugetheories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
28. [12] A. Fayyazuddin, Some comments on N = 2 supersymmetric Yang-Mills, Mod. Phys. Lett. A 10 (1995)2703, hep-th/9504120; S. Sethi, M. Stern and E. Zaslow, Monopole and dyon bound states in N = 2 supersymmetric Yang-Millstheories, Nucl. Phys. B 457 (1995) 484, hep-th/9508117; J.P. Gauntlett and J.A. Harvey, S-duality and dyon spectrum in N = 2 super Yang-Mills theory, Nucl.Phys. B 463 (1996) 287, hep-th 9508156; F. Ferrari and A. Bilal, The strong-coupling spectrum of the Seiberg-Witten theory, Nucl. Phys. B 469(1996) 387, hep-th/9602082; A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Self-dual strings and N = 2 supersymmetricfield theory, Nucl. Phys. B 477 (1996) 746, hep-th/9604034; F. Ferrari and A. Bilal, Curves of marginal stability and weak and strong coupling BPS spectra in N = 2supersymmetric QCD, Nucl. Phys. 480 (1996) 589, hep-th/9605101; A. Brandhuber and S. Steiberger, Self-dual strings and stability of BPS states in N = 2 SU(2) gauge theories, Nucl. Phys. B 488 (1997) 199, hep-th/9610053.
29. [13] A. Fayyazuddin, Results in supersymmetric field theory from 3-brane probe in F-theory, Nucl. Phys. B 497 (1997) 101, hep-th/9701185.
30. [14] M.R. Gaberdiel, T. Hauer and B. Zweibach, Open string-string junction transitions, Nucl. Phys. B 525 (1998) 117, hep-th/9801205.
31. [15] O. Bergmann and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys. B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl.Phys. B 531 (1998) 345, hep-th/9803142; O. De Wolfe and B. Zweibach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B541 (1999) 509, hep-th/9804210; O. De Wolfe, T. Hauer, A. Iqbal and B. Zweibach, Constraints on the BPS spectrum of N = 2, D = 4theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220; A. Iqbal, Self-intersection number of BPS junctions in backgrounds of three and sevenbranes, hep-th/9807117.
32. [15] O. Bergmann and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys.B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl. Phys. B 531 (1998) 345, hep-th/9803142; O. De Wolfe and B. Zweibach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B541 (1999) 509, hep-th/9804210; O. De Wolfe, T. Hauer, A. Iqbal and B. Zweibach, Constraints on the BPS spectrum of N = 2, D = 4theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220; A. Iqbal, Self-intersection number of BPS junctions in backgrounds of three and sevenbranes, hep-th/9807117.
33. [15] O. Bergmann and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys.B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl.Phys. B 531 (1998) 345, hep-th/9803142; O. De Wolfe and B. Zweibach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B 541 (1999) 509, hep-th/9804210; O. De Wolfe, T. Hauer, A. Iqbal and B. Zweibach, Constraints on the BPS spectrum of N = 2, D = 4theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220; A. Iqbal, Self-intersection number of BPS junctions in backgrounds of three and sevenbranes, hep-th/9807117.
34. [15] O. Bergmann and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys.B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl.Phys. B 531 (1998) 345, hep-th/9803142; O. De Wolfe and B. Zweibach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B541 (1999) 509, hep-th/9804210; O. De Wolfe, T. Hauer, A. Iqbal and B. Zweibach, Constraints on the BPS spectrum of N = 2, D = 4 theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220; A. Iqbal, Self-intersection number of BPS junctions in backgrounds of three and sevenbranes, hep-th/9807117.
35. [15] O. Bergmann and A. Fayyazuddin, String junctions and BPS states in Seiberg-Witten theory, Nucl. Phys.B 531 (1998) 108, hep-th/9802033; A. Mikhailov, N. Nekrasov and S. Sethi, Geometric realizations of BPS states in N = 2 theories, Nucl.Phys. B 531 (1998) 345, hep-th/9803142; O. De Wolfe and B. Zweibach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B541 (1999) 509, hep-th/9804210; O. De Wolfe, T. Hauer, A. Iqbal and B. Zweibach, Constraints on the BPS spectrum of N = 2, D = 4theories with A-D-E flavor symmetry, Nucl. Phys. B 534 (1998) 261, hep-th/9805220; A. Iqbal, Self-intersection number of BPS junctions in backgrounds of three and sevenbranes, hep-th/9807117.
36. [16] N.D. Lambert and P.C. West, Monopole dynamics from the M-theory fivebrane, hep-th/9811025.
37. [17] A. Fayyazuddin and M. Spalinski, Large-N superconformai gauge theories and supergravity orientifolds, Nucl. Phys. B 535 (1998) 219, hep-th/9805096.
38. [18] M.K. Prasad and C.M. Sommerfeld, An exact classical solution for the 't Hooft monopole and the Julia-Zee dyon, Phys. Rev. Lett. 35 (1975) 760.
39. [19] E. Witten and L. Susskind, The holographic bound in anti-de Sitter space, hep-th/9805114.
40. [20] N.S. Manton, A remark on the scattering of BPS monopoles, Phys. Lett. B 110 (1982) 54; N.S. Manton, Monopole interactions at long range, Phys. Lett. B 154 (1985) 395; B 157 (1985) 475(E).
41. [20] N.S. Manton, A remark on the scattering of BPS monopoles, Phys. Lett. B 110 (1982) 54; N.S. Manton, Monopole interactions at long range, Phys. Lett. B 154 (1985) 395; B 157 (1985) 475(E).
42. [20] N.S. Manton, A remark on the scattering of BPS monopoles, Phys. Lett. B 110 (1982) 54; N.S. Manton, Monopole interactions at long range, Phys. Lett. B 154 (1985) 395; B 157 (1985) 475 (E).
43. [21] A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformai symmetry in D-particle dynamics, Nucl. Phys. B 535 (1998) 335, hep-th/9805069; A. Jevicki, Y. Kazama and T. Yoneya, Quantum metamorphosis of conformai transformation in D3 brane Yang-Mills theory, Phys. Rev. Lett. 81 (1998) 5072, hep-th/9808039; A. Jevicki, Y. Kazama and T. Yoneya, Generalized conformai symmetry in D brane matrix models, Phys. Rev. D 59 (1999) 066001, hep-th/9810146; F. Gonzalez-Rey, B. Kulik, I.Y. Park and M. Rocek, Self-dual effective action of N = 4 super Yang-Mills, hep-th/9810152.
44. [21] A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformai symmetry in D-particle dynamics, Nucl. Phys. B 535 (1998) 335, hep-th/9805069;
45. [21] A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformai symmetry in D-particle dynamics, Nucl. Phys. B 535 (1998) 335, hep-th/9805069;
46. [21] A. Jevicki and T. Yoneya, Space-time uncertainty principle and conformai symmetry in D-particle dynamics, Nucl. Phys. B 535 (1998) 335, hep-th/9805069;
47. [22] B.R. Greene, A. Shapere, C. Vafa and S.T. Yau, Stringy cosmic strings and non-compact Calabi-Yau manifolds, Nucl. Phys. B 337 (1990) 1; M. Asano, Stringy cosmic strings and compactifications of F-theory, Nucl. Phys. B 503 (1997) 177,hep-th/9703070.
48. [22] B.R. Greene, A. Shapere, C. Vafa and S.T. Yau, Stringy cosmic strings and non-compact Calabi-Yaumanifolds, Nucl. Phys. B 337 (1990) 1; M. Asano, Stringy cosmic strings and compactifications of F-theory, Nucl. Phys. B 503 (1997) 177, hep-th/9703070.
49. [23] W. Lerche, Introduction to Seiberg-Witten theory and its stringy origin, Nucl. Phys. B (Proc. Suppl.) B 55 (1997) 83, hep-th/9611190.
50. [24] E. Witten, New perspectives in the quest for unification, hep-th 9812208; I. Klebanov, From threebranes to large-N gauge theories, hep-th 9901018.
51. [24] E. Witten, New perspectives in the quest for unification, hep-th 9812208; I. Klebanov, From threebranes to large-N gauge theories, hep-th 9901018.
52. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constantself-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonicgravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett.B 449 (1999) 39.
53. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constantself-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonicgravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett.B 449 (1999) 39.
54. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constant self-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonicgravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett.B 449 (1999) 39.
55. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constantself-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonicgravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett.B 449 (1999) 39.
56. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constantself-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonic gravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett.B 449 (1999) 39.
57. [25] A. Kehagias and K. Sfetsos, On running couplings in gauge theories from IIB supergravity, hep-th/9902125; S.S. Gubser, Dilaton-driven confinement, hep-th/9902155; H. Liu and A.A. Tseytlin, D3-brane-D-instanton configuration and N = 4 super YM theory in constantself-dual background, hep-th/9903091; A. Kehagias and K. Sfetsos, On asymptotic freedom and confinement from type IIB supergravity, hep-th/9903109; S. Noriji and S.D. Odinstov, Running gauge coupling and quark-antiquark potential from dilatonicgravity, hep-th/9904036; S. Nojiri and S.D. Odinstiv, Two-boundaries AdS/CFT correspondence in dilatonic gravity, Phys. Lett. B 449 (1999) 39.
58. [26] A.A. Tseytlin, Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory, Nucl. Phys. B 469 (1996) 51, hep-th/9602064; M. Aganic, J. Park, C. Popescu and J. Schwarz, Dual D-brane actions, Nucl. Phys. B 496 (1997) 215,hep-th/9702133.
59. [26] A.A. Tseytlin, Self-duality of Born-Infeld action and Dirichlet 3-brane of type IIB superstring theory,Nucl. Phys. B 469 (1996) 51, hep-th/9602064; M. Aganic, J. Park, C. Popescu and J. Schwarz, Dual D-brane actions, Nucl. Phys. B 496 (1997) 215, hep-th/9702133.
60. [27] M.B. Green and M. Gutperle, Comments on threebranes, Phys. Lett. B 377 (1996) 28, hep-th/9602077; D.E. Diaconescu, D-branes, monopoles and Nahm's equations, Nucl. Phys. B 503 (1997) 220, hep-th/9608163.
61. [27] M.B. Green and M. Gutperle, Comments on threebranes, Phys. Lett. B 377 (1996) 28, hep-th/9602077; D.E. Diaconescu, D-branes, monopoles and Nahm's equations, Nucl. Phys. B 503 (1997) 220, hep-th/9608163.
62. [28] C.G. Callan and J.M. Maldacena, Brane dynamics from the Born-Infeld action, Nucl. Phys. B 513 (1998) 198, hep-th/9708147; G.W. Gibbons, Born-Infeld particles and Dirichlet p-branes, Nucl. Phys. B 514 (1998) 603, hep-th/9709027.
63. [28] C.G. Callan and J.M. Maldacena, Brane dynamics from the Born-Infeld action, Nucl. Phys. B 513(1998) 198, hep-th/9708147; G.W. Gibbons, Born-Infeld particles and Dirichlet p-branes, Nucl. Phys. B 514 (1998) 603, hep-th/9709027.
64. [29] A. Hashimoto, Shape of branes pulled by strings, Phys. Rev. D 57 (1998) 6441, hep-th/9711097.
65. [30] G. Chalmers, M. Rocek and R. Von Unge, Monopoles in quantum corrected N = 2 super Yang-Mills theory, hep-th/9612195.
66. [31] For a nice review see J.A. Harvey, Magnetic monopoles, duality and supersymmetry, hep-th/9603086.
67. [32] F. Denef, Attractors at weak gravity, hep-th/9812049.
68. [33] P. Forgacs, Z. Horvath and L. Palla, Non-linear superposition of monopoles, Nucl. Phys. B 192 (1981) 141; M.K. Prasad, Exact Yang-Mills Higgs monopole solutions of arbitrary topological charge, Commun.Math. Phys. 80 (1981) 137.
69. [33] P. Forgacs, Z. Horvath and L. Palla, Non-linear superposition of monopoles, Nucl. Phys. B 192 (1981)141; M.K. Prasad, Exact Yang-Mills Higgs monopole solutions of arbitrary topological charge, Commun. Math. Phys. 80 (1981) 137.
70. [34] E. Weinberg, Parameter counting for multi-monopole solutions, Phys. Rev. D 20 (1979) 936; E. Corrigan and P. Goddard, An N monopole solution with 4N - 1 degrees of freedom, Commun. Math.Phys. 80 (1981) 575.
71. [34] E. Weinberg, Parameter counting for multi-monopole solutions, Phys. Rev. D 20 (1979) 936; E. Corrigan and P. Goddard, An N monopole solution with 4N - 1 degrees of freedom, Commun. Math. Phys. 80 (1981) 575.
72. [35] J.P. Gauntlett, Low energy dynamics of N = 2 supersymmetric monopoles, Nucl. Phys. B 411 (1994) 443, hep-th/9305068.
73. [36] G.W. Gibbons and N.S. Manton, Classical and quantum dynamics of BPS monopoles, Nucl. Phys. B 274 (1986) 183; G.W. Gibbons and N.S. Manton, The moduli space metric for well separated BPS monopoles, Phys.Lett. B 356 (1995) 32, hep-th/9506052.
74. [36] G.W. Gibbons and N.S. Manton, Classical and quantum dynamics of BPS monopoles, Nucl. Phys. B274 (1986) 183; G.W. Gibbons and N.S. Manton, The moduli space metric for well separated BPS monopoles, Phys. Lett. B 356 (1995) 32, hep-th/9506052.
75. [37] G. Gibbons, G. Papadopoulos and K. Stelle, HKT and OKT geometries on soliton black hole moduli spaces, Nucl. Phys. B 508 (1997) 623, hep-th/9706207.
76. [38] M.F. Atiyah and N.J. Hitchin, The Geometry and Dynamics of Magnetic Monopoles (Princeton Univ. Press, Princeton, 1988).
77. [39] H.W. Braden and P.M. Sutcliffe, A monopole metric, Phys. Lett. B 391 (1997) 366, hep-th/9610141; P. Sutcliffe, BPS monopoles, Int.J. Mod. Phys. A 12 (1997) 4663, hep-th/9707009.
78. [39] H.W. Braden and P.M. Sutcliffe, A monopole metric, Phys. Lett. B 391 (1997) 366, hep-th/9610141; P. Sutcliffe, BPS monopoles, Int.J. Mod. Phys. A 12 (1997) 4663, hep-th/9707009.
79. [40] R. Bielawski, Monopoles and the Gibbons-Manton metric. Commun. Math. Phys. 194 (1998) 297, hep-th/9801091.
80. [41] J.P. Gauntlett, C. Koehl, D. Mateos, P.K. Townsend and M. Zamaklar, Finite energy Dirac-Born-Infeld monopoles and string junctions, hep-th/9903156.