Skip to main content
SpringerLink
Log in

Noncommutative Instantons Revisited

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We find a new gauge in which U(1) noncommutative instantons are explicitly non-singular on noncommutative R 4. We also present a pedagogical introduction into noncommutative gauge theories.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Snyder, H.S.: Quantized Space-Time. Phys. Rev. 71, 38 (1947);§nyder, H.S.: The Electromagnetic Field in Quantized Space-Time. Phys. Rev. 72, 68 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  2. Connes, A.: Noncommutative geometry. London: Academic Press, 1994

  3. Gonzalez-Arroyo, A., Korthals Altes, C.P.: Reduced model for large N continuum field theories. Phys. Lett. 131B, 396 (1983)

    Article  Google Scholar 

  4. Filk, T.: Divergencies in a Field Theory on Quantum Space. Phys. Lett. 376B, 53 (1996)

    Article  MathSciNet  Google Scholar 

  5. Connes, A., Douglas, M., Schwarz, A.: JHEP 9802, 003 (1998)

  6. Douglas, M., Hull, C.: D-branes and the Noncommutative Torus. hep-th/9711165, JHEP 9802, 008 (1998)

  7. Kontsevich, M.: Deformation quantization of Poisson manifolds. q-alg/9709040

  8. Cattaneo, A., Felder, G.: A Path Integral Approach to the Konstevich Quantization Formula. math.QA/9902090

  9. Witten, E.: Nucl. Phys. B268, 253 (1986)

  10. Schomerus, V.: D-Branes and Deformation Quantization. JHEP 9906, 030 (1999)

    Google Scholar 

  11. Nekrasov, N., Schwarz, A.S.: hep-th/9802068 Commun. Math. Phys. 198, 689 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  12. Losev, A., Moore, G., Nekrasov, N., Shatashvili, S.: Four dimensional avatars of two dimensional RCFT. hep-th/9509151, Nucl. Phys. Proc. Suppl. 46, 130–145 (1996)

    Google Scholar 

  13. Harvey, J.A., Moore, G.: Algebras, BPS States, and Strings. hep-th/9510182, Nucl. Phys. B463, 315–368 (1996)

    Google Scholar 

  14. Losev, A., Nekrasov, N., Shatashvili, S.: The Freckled Instantons. In: The many faces of the superworld: Yuri golfand memorial volume, Ed. by M. Shifman, River Edge, NJ: World Scientific, 2000

  15. Hitchin, N.J., Karlhede, A., Lindstrom, U., Rocek, M.: Commun. Math. Phys. 108, 535 (1987)

    MathSciNet  MATH  Google Scholar 

  16. Callan, C.G., Jr., Maldacena, J.M.: Nucl. Phys. B513, 198–212 (1998) hep-th/9708147

  17. Bak, D.: Phys. Lett. 471B, 149–154 (1999) hep-th/9910135

    Article  MathSciNet  MATH  Google Scholar 

  18. Moriyama, S.: hep-th/0003231

  19. Mateos, D.: Noncommutative vs. commutative descriptions of D-brane BIons. hep-th/0002020

  20. Gopakumar, R., Minwala, S., Strominger, A.: hep-th/0003160, JHEP 0005, 020 (2000)

  21. Losev, A., Moore, G., Shatashvili, S.: M&m's. hep-th/9707250 Nucl. Phys. B522, 105–124 (1998)

    Google Scholar 

  22. Ho, P.-M.: hep-th/0003012

  23. Gross, D., Nekrasov, N.: Monopoles and strings in noncommutative gauge theory. hep-th/9905204

  24. Polychronakos, A.P.: Flux tube solutions in noncommutative gauge theories. hep-th/0007043

  25. Gross, D., Nekrasov, N.: Dynamics of strings in noncommutative gauge theory. hep-th/9907204

  26. Gross, D., Nekrasov, N.: Solitons in noncommutative gauge theories. To appear

  27. Corrigan, E., Goddard, P.: Construction of instanton and monopole solutions and reciprocity. Ann. Phys. 154, 253 (1984)

    MathSciNet  MATH  Google Scholar 

  28. Aganagic, M., Gopakumar, R., Minwalla, S., Strominger, A.: Unstable Solitons in Noncommutative Gauge Theory. hep-th/0009142

  29. Donaldson, S.K.: Instantons and Geometric Invariant Theory. Commun. Math. Phys. 93, 453–460 (1984)

    MathSciNet  MATH  Google Scholar 

  30. Nakajima, H.: Lectures on Hilbert Schemes of Points on Surfaces. AMS University Lecture Series, Providence, RI: Aus, 1999, ISBN 0-8218-1956-9

  31. Braden, H., Nekrasov, N.: hep-th/9912019

  32. Furuuchi, K.: hep-th/9912047

  33. Furuuchi, K.: hep-th/0010006

  34. Aharony, O., Berkooz, M., Seiberg, N.: hep-th/9712117, Adv. Theor. Math. Phys. 2, 119–153 (1998)

    MathSciNet  MATH  Google Scholar 

  35. Aharony, O., Berkooz, M., Kachru, S., Seiberg, N., Silverstein, E.: hep-th/9707079, Adv. Theor. Math. Phys. 1, 148–157 (1998)

    MATH  Google Scholar 

  36. Seiberg, N., Witten, E.: hep-th/9908142, JHEP 9909, 032 (1999)

  37. Strominger, A., Vafa, C.: Microscopic Origin of the Bekenstein-Hawking Entropy. hep-th/9601029, Phys. Lett. 379, 99–104 (1996)

    Google Scholar 

  38. Vafa, C., Witten, E.: A Strong Coupling Test of S-Duality. hep-th/9408074, Nucl. Phys. B431, 3–77 (1994)

  39. Teo, E., Ting, C.: Monopoles, vortices and kinks in the framework of noncommutative geometry. Phys. Rev. D56, 2291–2302 (1997), hep-th/9706101

    Google Scholar 

  40. Diaconescu, D.-E.: Nucl. Phys. B503, 220–238 (1997) hep-th/9608163

  41. Terashima, S.: Instantons in the U(1) Born-Infeld Theory and Noncommutative Gauge Theory. hep-th/9911245, Phys. Lett. 477B, 292–298 (2000)

    Google Scholar 

  42. Jiang, L.: Dirac Monopole in Non-Commutative Space. hep-th/0001073

  43. Hashimoto, K., Hata, H., Moriyama, S.: hep-th/9910196, JHEP 9912, 021 (1999); Hashimoto, A., Hashimoto, K.: hep-th/9909202, JHEP 9911, 005 (1999) Hashimoto, K., Hirayama, T.: hep-th/0002090

  44. Harvey, J., Kraus, P., Larsen, F., Martinec, E.: hep-th/0005031

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, 117259, Moscow, Russia

    Nikita A. Nekrasov

  2. Joseph Henry Laboratories, Princeton University, Princeton, NJ, 08544, USA

    Nikita A. Nekrasov

  3. IHES, Le Bois-Marie, 35 route de Chartres, 91440, Bures-sur-Yvette, France

    Nikita A. Nekrasov

Authors
  1. Nikita A. Nekrasov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by M.R. Douglas

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nekrasov, N. Noncommutative Instantons Revisited. Commun. Math. Phys. 241, 143–160 (2003). https://doi.org/10.1007/s00220-003-0911-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-003-0911-8

Keywords

Search

Navigation