Skip to main content
SpringerLink
Log in

Non-Abelian Conifold Transitions and N = 4 Dualities in Three Dimensions

  • Chapter
Topological Field Theory, Primitive Forms and Related Topics

Part of the book series: Progress in Mathematics ((PM,volume 160))

  • 840 Accesses

Abstract

We show how the Higgs mechanism for non-abelian N = 2 gauge theories in four dimensions is geometrically realized in the context of type II strings as transitions among compactifications of Calabi-Yau threefolds. We use this result and T-duality of a further compacitification on a circle to derive N = 4, d = 3 dual field theories. This reduces dualities for N = 4 gauge systems in three dimensions to perturbative symmetries of string theory. Moreover, we find that the dual of a gauge system always exists but may or may not correspond to a lagrangian system. In particular, we verify a conjecture of Intriligator and Seiberg that an ordinary gauge system is dual to compacitification of exceptional tensionless string theory down to three dimensions.

HUTP-97/A024, LBNL-40349, UCB-PTH-97/27 hep-th/9705220

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. Witten, Nucl. Phys. B443 (1995) 85, hep-th/9503124.

    Article  MathSciNet  Google Scholar 

  2. M. Duff, Nucl. Phys. B442 (1995) 47, hep-th/9501030.

    MathSciNet  Google Scholar 

  3. S. Katz, A. Klemm and C. Vafa, hep-th/9609239.

    Google Scholar 

  4. S. Katz, P. Mayr and C. Vafa, to appear.

    Google Scholar 

  5. S. Katz and C. Vafa, hep-th/9611090.

    Google Scholar 

  6. M. Bershadsky, A. Johansen, T. Pantev, V. Sadov and C. Vafa, hepth/9612052; C. Vafa and B. Zwiebach, hep-th/9701015.

    Google Scholar 

  7. H. Ooguri and C. Vafa, hep-th/9702180, to appear in Nucl. Phys. B.

    Google Scholar 

  8. C. Ahn and K. Oh, hep-th/9704061.

    Google Scholar 

  9. C. Ahn, hep-th/9705004.

    Google Scholar 

  10. M. Douglas, S. Katz and C. Vafa, hep-th/9609071.

    Google Scholar 

  11. D. R. Morrison and N. Seiberg, Nucl. Phys. B483 (1997) 229, hep-th/9609070.

    Article  MathSciNet  Google Scholar 

  12. K. Intriligator, D. R. Morrison and N. Seiberg, hep-th/9702198.

    Google Scholar 

  13. E. Witten, Nucl. Phys. B471 (1996) 121, hep-th/9603003.

    MathSciNet  Google Scholar 

  14. M. Bershadsky and C. Vafa, hep-th/9703167.

    Google Scholar 

  15. K. Intriligator, hep-th/9702038; J. D. Blum and K. Intriligator, hep-th/9705030, hep-th/9705044.

    Google Scholar 

  16. P. Aspinwall and D. R. Morrison, hep-th/9705104.

    Google Scholar 

  17. A. Hanany and E. Witten, hep-th/9611230.

    Google Scholar 

  18. J. de Boer, K. Hori, H. Ooguri, Y. Oz and Z. Yin, hep-th/9612131, to appear in Nucl. Phys. B.

    Google Scholar 

  19. S. Elitzur, A. Giveon and D. Kutasov, hep-th/9702014.

    Google Scholar 

  20. J. de Boer, K. Hori, Y. Oz and Z. Yin, hep-th/9702154.

    Google Scholar 

  21. J. de Boer, K. Hori and Y. Oz, hep-th/9703100.

    Google Scholar 

  22. O. Aharony, A. Hanany, K. Intriligator, N. Seiberg, M. J. Strassler, hep-th/9703110.

    Google Scholar 

  23. N. Evans, C. V. Johnson, A. D. Shapere, hep-th/9703210.

    Google Scholar 

  24. J. H. Brodie, A. Hanany, hep-th/9704043.

    Google Scholar 

  25. A. Brandhuber, J. Sonnenschein, S. Theisen and S. Yankielowicz, hep-th/9704044.

    Google Scholar 

  26. S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and D. Kutasov, hep-th/9704104.

    Google Scholar 

  27. O. Aharony and A. Hanany, hep-th/9704170.

    Google Scholar 

  28. H. Ooguri and C. Vafa, Nucl. Phys. B463 (1996) 55, hep-th/9511164.

    Article  MathSciNet  Google Scholar 

  29. K. Intriligator and N. Seiberg, Phys. Lett. B387 (1996) 513.

    MathSciNet  Google Scholar 

  30. J. de Boer, K. Hori, H. Ooguri and Y. Oz, hep-th/9611063, to appear in Nucl. Phys. B.

    Google Scholar 

  31. M. Porrati and A. Zaffaroni, hep-th/9611201.

    Google Scholar 

  32. A. Klemm and P. Mayr, hep-th/9601014.

    Google Scholar 

  33. S. Katz, D. R. Morrison and M. R. Plesser, Nucl. Phys. B477 (1996) 105, hep-th/9601108.

    Article  MathSciNet  Google Scholar 

  34. M. Bershadsky, K. Intriligator, S. Kachru, D. R. Morrison, V. Sadov, and C. Vafa, Nucl. Phys. B481 (1996) 215, hep-th/9605200.

    Article  MathSciNet  Google Scholar 

  35. S. Katz and C. Vafa, hep-th/9606086.

    Google Scholar 

  36. P. Berglund, S. Katz, A. Klemm, P. Mayr, Nucl. Phys. B483 (1997) 209, hep-th/9605154.

    Article  MathSciNet  Google Scholar 

  37. M. Bershadsky, V. Sadov and C. Vafa, Nucl. Phys. B463 (1996) 398, hep-th/9510225.

    Article  MathSciNet  Google Scholar 

  38. A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Nucl. Phys. B477 (1996) 746, hep-th/9604034.

    Article  MathSciNet  Google Scholar 

  39. N. Seiberg and S. Shenker, Phys. Lett. B388 (1996) 521, hep-th/9608086.

    MathSciNet  Google Scholar 

  40. A. Strominger, Nucl. Phys. B451 (1995) 96, hep-th/9504090.

    Article  MathSciNet  Google Scholar 

  41. B. Greene, D. R. Morrison and A. Strominger, Nucl.Phys. B451 (1995) 109, hep-th/9504145.

    Article  MathSciNet  Google Scholar 

  42. Articles in “Essays on Mirror Manifolds,” edited by S.-T. Yau, International Press, 1992.

    Google Scholar 

  43. M. Kontsevich, Proceedings of ICM, Zürich 1994, alg-geom/9411018.

    Google Scholar 

  44. A. Givental, alg-geom/9603021, alg-geom/9701016.

    Google Scholar 

  45. A. Strominger, S.-T. Yau and E. Zaslow, Nucl. Phys. B 479 (1996) 243, hep-th/9606040.

    Article  MathSciNet  Google Scholar 

  46. D. R. Morrison, alg-geom/9608006.

    Google Scholar 

  47. M. Gross and P.M.H. Wilson, alg-geom/9608004.

    Google Scholar 

  48. C. Vafa and E. Witten, J. Geom. Phys. 15 (1995) 189, hep-th/9409188.

    Article  MathSciNet  MATH  Google Scholar 

  49. B. Greene, D. R. Morrison and C. Vafa, Nucl. Phys. B481 (1996) 513, hep-th/9608039.

    Article  MathSciNet  Google Scholar 

  50. P. Candelas, P. S. Green and T. Hübsch, Phys. Rev. Lett. 62 (1989) 1956.

    Article  MathSciNet  Google Scholar 

  51. M. Bershadsky and A. Johansen, Nucl. Phys. B489 (1997) 122.

    Article  MathSciNet  Google Scholar 

  52. R. Friedman, J. Morgan and E. Witten, hep-th/9701162.

    Google Scholar 

  53. J.A. Minahan and D. Nemeschansky, Nucl. Phys. B489 (1997) 24, hep-th/9608047; Nucl. Phys. B482 (1996) 142, hep-th/9610076.

    Article  MathSciNet  Google Scholar 

  54. O.J. Ganor, D.R. Morrison and N. Seiberg, Nucl. Phys. B487 (1997) 93, hep-th/9610251.

    Article  MathSciNet  Google Scholar 

  55. W. Lerche, P. Mayr and N. Warner, hep-th/9612085.

    Google Scholar 

  56. E. Verlinde, Nucl. Phys. B455 (1995) 211, hep-th/9506011.

    Article  MathSciNet  Google Scholar 

  57. E. Witten, hep-th/9703166.

    Google Scholar 

  58. S. Katz and D.R. Morrison, Journ. Alg. Geom. 1 (1992) 449.

    MathSciNet  MATH  Google Scholar 

  59. P.C. Argyres and A.D. Shapere, Nucl. Phys. B461 (1996) 437, hep-th/9509175.

    Article  MathSciNet  Google Scholar 

  60. P.C. Argyres, M.R. Plesser and N. Seiberg, Nucl. Phys. B471 (1996) 159, hep-th/9603042.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, 366 Le Conte Hall, Berkeley, CA, 94720-7300, USA

    Kentaro Hori & Hirosi Ooguri

  2. Theoretical Physics Group, Ernest Orlando Lawrence Berkeley National Laboratory, Mail Stop 50A-5101, Berkeley, CA, 94720, USA

    Kentaro Hori & Hirosi Ooguri

  3. Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA

    Cumrun Vafa

Authors
  1. Kentaro Hori
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hirosi Ooguri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cumrun Vafa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-01, Japan

    Masaki Kashiwara  & Kyoji Saito  & 

  2. Department of Mathematical Sciences, University of Tokyo, Tokyo, 153, Japan

    Atsushi Matsuo

  3. Department of Mathematics, Osaka University, Toyonaka-city, 560, Japan

    Ikuo Satake

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Hori, K., Ooguri, H., Vafa, C. (1998). Non-Abelian Conifold Transitions and N = 4 Dualities in Three Dimensions. In: Kashiwara, M., Matsuo, A., Saito, K., Satake, I. (eds) Topological Field Theory, Primitive Forms and Related Topics. Progress in Mathematics, vol 160. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0705-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-0705-4_7

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6874-1

  • Online ISBN: 978-1-4612-0705-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation