Skip to main content

Equivalence of geometric engineering and Hanany-Witten

  • Conference paper
  • First Online:
Quantum Aspects of Gauge Theories, Supersymmetry and Unification

Part of the book series: Lecture Notes in Physics ((LNP,volume 525))

  • 477 Accesses

Abstract

We show the equivalence of three different realisations of gauge theory in string theory. These are the Hanany-Witten brane constructions, the use of branes as probes and geometric engineering. We illustrate the equivalence via T- and S-dualities with the simplest non-trivial examples in four dimensions: N=2 SYM with gauge groups Π SU(N i ).

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Karch, A., Lüst, D., Smith, D.J. Equivalence of geometric engineering and Hanany-Witten via fractional branes Nucl. Phys. B533 (1998) 348–372; hep-th/9803232

    Article  ADS  Google Scholar 

  2. Hanany, A., Witten, E. Type IIB Superstrings, BPS monopoles, and three-dimensional gauge dynamics Nucl. Phys. B492 (1997) 152–190; hep-th/9611230

    Article  ADS  MathSciNet  Google Scholar 

  3. Douglas, M.R., Moore, G. D-branes, quivers, and ALE instantons hep-th/9603167

    Google Scholar 

  4. Klemm, A., Lerche, W., Mayr, P., Vafa, C., Warner, N. Selfdual strings and N-2 supersymmetric field theory Nucl. Phys. B477 (1996) 746–766; hep-th/9604034

    Article  ADS  MathSciNet  Google Scholar 

  5. Katz, S., Klemm, A., Vafa, C. Geometric engineering of quantum field theories Nucl. Phys. B497 (1997) 173–195; hep-th/9609239

    Article  ADS  MathSciNet  Google Scholar 

  6. Katz, S., Mayr, P., Vafa, C. Mirror symmetry and exact solution of 4-D N=2 gauge theories — I Adv. Theor. Math. Phys. 1 (1998) 53–114; hep-th/9706110

    MathSciNet  Google Scholar 

  7. Polchinski, J. Tensors from K3 orientifolds Phys. Rev. D55 (1997) 6423–6428; hep-th/9606165

    ADS  MathSciNet  Google Scholar 

  8. Douglas, M.R. Enhanced gauge symmetry in M(atrix) theory J. High Energy Phys. 07 (1997) 004; hep-th/9612126

    Article  ADS  Google Scholar 

  9. Diaconescu, D.-E., Douglas, M.R., Gomis, J. Fractional branes and wrapped branes J. High Energy Phys. 02 (1998) 013; hep-th/9712230

    Article  ADS  MathSciNet  Google Scholar 

  10. Witten, E. Solutions of four-dimensional field theories via M theory Nucl. Phys. B500 (1997) 3–42; hep-th/9703166

    Article  ADS  MathSciNet  Google Scholar 

  11. Ooguri, H., Vafa, C. Two-dimensional black hole and singularities of CY manifolds Nucl. Phys. B463 (1996) 55–72; hep-th/9511164

    Article  ADS  MathSciNet  Google Scholar 

  12. Lawrence, A., Nekrasov, N., Vafa, C. On conformal field theories in four-dimensions Nucl. Phys. B533 (1998) 199–209; hep-th/9803015

    Article  ADS  MathSciNet  Google Scholar 

  13. Brodie, J. Fractional branes, confinement, and dynamically generated superpotentials Nucl. Phys. B532 (1998) 137–152; hep-th/9803140

    Article  ADS  MathSciNet  Google Scholar 

  14. Hanany, A., Zaffaroni, A. On the realization of chiral four-dimensional gauge theories using branes J. High Energy Phys. 05 (1998) 001; hep-th/9801134

    Article  ADS  MathSciNet  Google Scholar 

  15. Hanany, A., Uranga, A.M. Brane boxes and branes on singularities J. High Energy Phys. 05 (1998) 013; hep-th/9805139

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. Ceresole C. Kounnas D. Lüst S. Theisen

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag

About this paper

Cite this paper

Smith, D.J. (1999). Equivalence of geometric engineering and Hanany-Witten. In: Ceresole, A., Kounnas, C., Lüst, D., Theisen, S. (eds) Quantum Aspects of Gauge Theories, Supersymmetry and Unification. Lecture Notes in Physics, vol 525. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104270

Download citation

  • DOI: https://doi.org/10.1007/BFb0104270

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66005-7

  • Online ISBN: 978-3-540-48792-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics