HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 126 (2011) > Number 4
| Next Article >

Prog. Theor. Phys. Vol. 126 No. 4 (2011) pp. 637-680

[ Full Text PDF : OPEN SELECT (397K) ]

Volume of Moduli Space of Vortex Equations and Localization

Akiko Miyake,1,2,* Kazutoshi Ohta2,** and Norisuke Sakai3,***

1Department of General Education, Kushiro National College of Technology, Kushiro 084-0916, Japan
2Institute of Physics, Meiji Gakuin University, Yokohama 244-8539, Japan
3Department of Mathematics, Tokyo Woman's Christian University, Tokyo 167-8585, Japan

(Received May 26, 2011; Revised August 17, 2011)

Abstract:

We evaluate volume of moduli space of BPS vortices on a compact genus h Riemann surface Σh by using topological field theory and localization technique developed by Moore, Nekrasov and Shatashvili. We apply this technique to Abelian (ANO) vortex and show that the volume of moduli space agrees with the previous results obtained by integrating over the moduli space metric. We extend the evaluation to non-Abelian gauge groups and multi-flavors. We also compare our results with the volume of the Kähler quotient space inspired by the brane configuration.

Subject Index : 134, 135
URL : http://ptp.ipap.jp/link?PTP/126/637/
DOI : 10.1143/PTP.126.637


*E-mail: miyake@ippan.kushiro-ct.ac.jp
**E-mail: kohta@law.meijigakuin.ac.jp
***E-mail: sakai@lab.twcu.ac.jp

[ Full Text PDF : OPEN SELECT (397K) ] Citation:

References:

  1. N. S. Manton and P. Sutcliffe, Topological Solitons (Cambridge University Press, UK, 2004), p. 493.
  2. N. S. Manton, Phys. Lett. B 110 (1982), 54[CrossRef].
  3. T. M. Samols, Commun. Math. Phys. 145 (1992), 149[CrossRef].
  4. N. S. Manton, Nucl. Phys. B 400 (1993), 624[CrossRef].
  5. P. A. Shah and N. S. Manton, J. Math. Phys. 35 (1994), 1171, [CrossRef] hep-th/9307165[e-print arXiv].
  6. N. A. Nekrasov, Adv. Theor. Math. Phys. 7 (2004), 831, hep-th/0206161[e-print arXiv].
  7. C. H. Taubes, Commun. Math. Phys. 72 (1980), 277[CrossRef].
  8. N. S. Manton and S. M. Nasir, Commun. Math. Phys. 199 (1999), 591, [CrossRef] hep-th/9807017[e-print arXiv].
  9. S. M. Nasir, Phys. Lett. B 419 (1998), 253, [CrossRef] hep-th/9807020[e-print arXiv].
  10. N. S. Manton and J. M. Speight, Commun. Math. Phys. 236 (2003), 535, [CrossRef] hep-th/0205307[e-print arXiv].
  11. H. Y. Chen and N. S. Manton, J. Math. Phys. 46 (2005), 052305, [CrossRef] hep-th/0407011[e-print arXiv].
  12. N. M. Romão, J. of Phys. A 38 (2005), 9127, [CrossRef] hep-th/0503014[e-print arXiv].
  13. A. Abrikosov, Sov. Phys. -JETP 32 (1957), 1442.
    H. Nielsen and P. Olesen, Nucl. Phys. B 61 (1973), 45[CrossRef].
  14. S. B. Bradlow, Commun. Math. Phys. 135 (1990), 1[CrossRef].
  15. N. S. Manton and N. M. Romão, arXiv:1010.0644[e-print arXiv].
  16. N. S. Manton and N. A. Rink, J. of Phys. A 43 (2010), 434024, [CrossRef] arXiv:0912.2058[e-print arXiv]; arXiv:1012.3014[e-print arXiv].
  17. A. Hanany and D. Tong, J. High Energy Phys. 07 (2003), 037, [CrossRef] hep-th/0306150[e-print arXiv]; J. High Energy Phys. 04 (2004), 066, [CrossRef] hep-th/0403158[e-print arXiv].
  18. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Phys. Rev. Lett. 96 (2006), 161601, [APS] hep-th/0511088[e-print arXiv].
  19. M. Eto, T. Fujimori, Y. Isozumi, M. Nitta, K. Ohashi, K. Ohta and N. Sakai, Phys. Rev. D 73 (2006), 085008, [APS] hep-th/0601181[e-print arXiv].
  20. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, J. of Phys. A 39 (2006), R315, [CrossRef] hep-th/0602170[e-print arXiv].
  21. M. Eto, Y. Isozumi, M. Nitta, K. Ohashi and N. Sakai, Phys. Rev. D 73 (2006), 125008, [APS] hep-th/0602289[e-print arXiv].
  22. M. Eto, J Evslin, K. Konishi, G. Marmorini, M. Nitta, K. Ohashi, W. Vinci and N. Yokoi, Phys. Rev. D 76 (2007), 105002, [APS] arXiv:0704.2218[e-print arXiv].
  23. M. Eto, T. Fujimori, M. Nitta, K. Ohashi, K. Ohta and N. Sakai, Nucl. Phys. B 788 (2008), 120, [CrossRef] hep-th/0703197[e-print arXiv].
  24. J. M. Baptista, Commun. Math. Phys. 291 (2009), 799, [CrossRef] arXiv:0810.3220[e-print arXiv].
  25. M. Eto, T. Fujimori, T. Nagashima, M. Nitta, K. Ohashi and N. Sakai, Phys. Lett. B 678 (2009), 254, [CrossRef] arXiv:0903.1518[e-print arXiv].
  26. N. S. Manton and N. Sakai, Phys. Lett. B 687 (2010), 395, [CrossRef] arXiv:1001.5236[e-print arXiv].
  27. T. Fujimori, G. Marmorini, M. Nitta, K. Ohashi and N. Sakai, Phys. Rev. D 82 (2010), 065005, [APS] arXiv:1002.4580[e-print arXiv].
  28. G. W. Moore, N. Nekrasov and S. Shatashvili, Commun. Math. Phys. 209 (2000), 97, [CrossRef] hep-th/9712241[e-print arXiv].
  29. A. A. Gerasimov and S. L. Shatashvili, Commun. Math. Phys. 277 (2008), 323, [CrossRef] hep-th/0609024[e-print arXiv].
  30. E. Witten, J. Geom. Phys. 9 (1992), 303, hep-th/9204083[e-print arXiv].
  31. M. Blau and G. Thompson, Nucl. Phys. B 408 (1993), 345, [CrossRef] hep-th/9305010[e-print arXiv]; hep-th/9310144[e-print arXiv].
  32. K. M. Lee and H. U. Yee, J. High Energy Phys. 03 (2007), 012, [CrossRef] hep-th/0605214[e-print arXiv].
    H. U. Yee, Nucl. Phys. B 774 (2007), 232, [CrossRef] hep-th/0612002[e-print arXiv].
  33. K. Fujii, J. Appl. Math. 2 (2002), 371.
  34. I. G. Macdonald, Inventiones Math. 56 (1980), 93.
  35. H. Ooguri and C. Vafa, Nucl. Phys. B 641 (2002), 3, [CrossRef] hep-th/0205297[e-print arXiv].
  36. M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics (Hilger, Bristol, UK, 1990), p. 505.
  37. N. J. Hitchin, A. Karlhede, U. Lindstrom and M. Rocek, Commun. Math. Phys. 108 (1987), 535[CrossRef].
  38. G. W. Moore, N. Nekrasov and S. Shatashvili, Commun. Math. Phys. 209 (2000), 77, [CrossRef] hep-th/9803265[e-print arXiv].
  39. S. Shadchin, J. High Energy Phys. 08 (2007), 052, [CrossRef] hep-th/0611278[e-print arXiv].
  40. K. Ohta, arXiv:0710.4011[e-print arXiv].
  41. T. Dimofte, S. Gukov and L. Hollands, arXiv:1006.0977[e-print arXiv].
  42. H. Awata, H. Fuji, H. Kanno, M. Manabe and Y. Yamada, arXiv:1008.0574[e-print arXiv].
  43. Y. Yoshida, arXiv:1101.0872[e-print arXiv].
  44. G. Bonelli, A. Tanzini and J. Zhao, arXiv:1102.0184[e-print arXiv].
  45. H. Nakajima, Lectures on Hilbert Schemes of Points on Surfaces, University Lectures Series Vol. 18 (American Mathematical Society, 1999).
  46. U. Bruzzo, F. Fucito, J. F. Morales and A. Tanzini, J. High Energy Phys. 05 (2003), 054, [CrossRef] hep-th/0211108[e-print arXiv].

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.