Skip to main content
SpringerLink
Log in

Hyperbolic Calorons, Monopoles, and Instantons

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

Abstract

We construct families of SO(3)-symmetric charge 1 instantons and calorons on the space \({\mathbb{H}^3 \times \mathbb{R}}\) . We show how the calorons include instantons and hyperbolic monopoles as limiting cases. We show how Euclidean calorons are the flat space limit of this family.

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.

Similar content being viewed by others

References

  1. Atiyah, M.F.: Magnetic monopoles in hyperbolic spaces. In: Vector Bundles on Algebraic Varieties, Oxford: Oxford University Press, 1087, pp. 1–34

  2. Chakrabarti, A.: Construction of hyeprbolic monopoles. J. Math. Phys. 27, 340–348 (1985)

    Article  ADS  Google Scholar 

  3. Corrigan, E., Fairlie, D.B.: Scalar field theory and exact solutions to a classical su(2)-gauge theory. Phys. Lett. 67B, 69–71 (1977)

    ADS  MathSciNet  Google Scholar 

  4. Garland, H., Murray, M.K.: Why instantons are monopoles. Commun. Math. Phys. 121, 85–90 (1989)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Gross, D.J., Pisarski, R.D., Yaffe, L.G.: Qcd and instantons at finite temperature. Rev. Mod. Phys. 53, 43 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  6. Harrington, B.J., Shepard, H.K.: Periodic euclidean solutions and the finite-temperature yang-mills gas. Phys. Rev. D17(8), 2122–2125 (1978)

    ADS  Google Scholar 

  7. Jaffe, A., Taubes, C.: Vortices and Monopoles. Birkhäuser, Boston (1980)

    MATH  Google Scholar 

  8. Kraan, T.C., van Baal, P.: Periodic instantons with non-trivial holonomy. Nucl. Phys. B533, 627–659 (1998)

    Article  ADS  Google Scholar 

  9. Landweber, G.D.: Singular instantons with so(3) symmetry. http://arxiv.org/math.dg/0503611, 2005

  10. Lee, K., Lu, C.: su(2) calorons and magnetic monopoles. Phys. Rev. D15, 025011 (1998)

    ADS  MathSciNet  Google Scholar 

  11. Manton, N.S.: Instantons on a line. Phys. Lett. 76B, 111–112 (1978)

    ADS  Google Scholar 

  12. Nash, C.: Geometry of hyperbolic monopoles. J. Math. Phys. 27, 2160–2164 (1986)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Norbury, P.: Asymptotic values of hyperbolic monopoles. J. Geom. Phys. 51, 13–33 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. Norbury, P., Jarvis, S.: Zero and infinite curvature limits of hyperbolic monopoles. Bull. of the L.M.S. 29, 737–744 (1997)

    Article  MathSciNet  Google Scholar 

  15. Rossi, P.: Propagation functions in the field of a monopole. Nucl. Phys. B149, 170–188 (1979)

    Article  ADS  Google Scholar 

  16. Witten, E.: Some exact multipseudoparticle solutions of classical yang-mills theory. Phys. Rev. Lett 38(3), 121–124 (1977)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham, DH1 3LE, UK

    Derek Harland

Authors
  1. Derek Harland
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Derek Harland.

Additional information

Communicated by G.W. Gibbons

Supported by PPARC.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Harland, D. Hyperbolic Calorons, Monopoles, and Instantons. Commun. Math. Phys. 280, 727–735 (2008). https://doi.org/10.1007/s00220-008-0471-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-008-0471-z

Keywords

Search

Navigation