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

  • Kentaro Hori
  • Hirosi Ooguri
  • Cumrun Vafa
Part of the Progress in Mathematics book series (PM, volume 160)


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.


Gauge Theory Gauge Group Coulomb Branch Dual Pair Rational Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    E. Witten, Nucl. Phys. B443 (1995) 85, hep-th/9503124.MathSciNetCrossRefGoogle Scholar
  2. [2]
    M. Duff, Nucl. Phys. B442 (1995) 47, hep-th/9501030.MathSciNetGoogle Scholar
  3. [3]
    S. Katz, A. Klemm and C. Vafa, hep-th/9609239.Google Scholar
  4. [4]
    S. Katz, P. Mayr and C. Vafa, to appear.Google Scholar
  5. [5]
    S. Katz and C. Vafa, hep-th/9611090.Google Scholar
  6. [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. [7]
    H. Ooguri and C. Vafa, hep-th/9702180, to appear in Nucl. Phys. B.Google Scholar
  8. [8]
    C. Ahn and K. Oh, hep-th/9704061.Google Scholar
  9. [9]
    C. Ahn, hep-th/9705004.Google Scholar
  10. [10]
    M. Douglas, S. Katz and C. Vafa, hep-th/9609071.Google Scholar
  11. [11]
    D. R. Morrison and N. Seiberg, Nucl. Phys. B483 (1997) 229, hep-th/9609070.MathSciNetCrossRefGoogle Scholar
  12. [12]
    K. Intriligator, D. R. Morrison and N. Seiberg, hep-th/9702198.Google Scholar
  13. [13]
    E. Witten, Nucl. Phys. B471 (1996) 121, hep-th/9603003.MathSciNetGoogle Scholar
  14. [14]
    M. Bershadsky and C. Vafa, hep-th/9703167.Google Scholar
  15. [15]
    K. Intriligator, hep-th/9702038; J. D. Blum and K. Intriligator, hep-th/9705030, hep-th/9705044.Google Scholar
  16. [16]
    P. Aspinwall and D. R. Morrison, hep-th/9705104.Google Scholar
  17. [17]
    A. Hanany and E. Witten, hep-th/9611230.Google Scholar
  18. [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. [19]
    S. Elitzur, A. Giveon and D. Kutasov, hep-th/9702014.Google Scholar
  20. [20]
    J. de Boer, K. Hori, Y. Oz and Z. Yin, hep-th/9702154.Google Scholar
  21. [21]
    J. de Boer, K. Hori and Y. Oz, hep-th/9703100.Google Scholar
  22. [22]
    O. Aharony, A. Hanany, K. Intriligator, N. Seiberg, M. J. Strassler, hep-th/9703110.Google Scholar
  23. [23]
    N. Evans, C. V. Johnson, A. D. Shapere, hep-th/9703210.Google Scholar
  24. [24]
    J. H. Brodie, A. Hanany, hep-th/9704043.Google Scholar
  25. [25]
    A. Brandhuber, J. Sonnenschein, S. Theisen and S. Yankielowicz, hep-th/9704044.Google Scholar
  26. [26]
    S. Elitzur, A. Giveon, E. Rabinovici, A. Schwimmer and D. Kutasov, hep-th/9704104.Google Scholar
  27. [27]
    O. Aharony and A. Hanany, hep-th/9704170.Google Scholar
  28. [28]
    H. Ooguri and C. Vafa, Nucl. Phys. B463 (1996) 55, hep-th/9511164.MathSciNetCrossRefGoogle Scholar
  29. [29]
    K. Intriligator and N. Seiberg, Phys. Lett. B387 (1996) 513.MathSciNetGoogle Scholar
  30. [30]
    J. de Boer, K. Hori, H. Ooguri and Y. Oz, hep-th/9611063, to appear in Nucl. Phys. B.Google Scholar
  31. [31]
    M. Porrati and A. Zaffaroni, hep-th/9611201.Google Scholar
  32. [32]
    A. Klemm and P. Mayr, hep-th/9601014.Google Scholar
  33. [33]
    S. Katz, D. R. Morrison and M. R. Plesser, Nucl. Phys. B477 (1996) 105, hep-th/9601108.MathSciNetCrossRefGoogle Scholar
  34. [34]
    M. Bershadsky, K. Intriligator, S. Kachru, D. R. Morrison, V. Sadov, and C. Vafa, Nucl. Phys. B481 (1996) 215, hep-th/9605200.MathSciNetCrossRefGoogle Scholar
  35. [35]
    S. Katz and C. Vafa, hep-th/9606086.Google Scholar
  36. [36]
    P. Berglund, S. Katz, A. Klemm, P. Mayr, Nucl. Phys. B483 (1997) 209, hep-th/9605154.MathSciNetCrossRefGoogle Scholar
  37. [37]
    M. Bershadsky, V. Sadov and C. Vafa, Nucl. Phys. B463 (1996) 398, hep-th/9510225.MathSciNetCrossRefGoogle Scholar
  38. [38]
    A. Klemm, W. Lerche, P. Mayr, C. Vafa and N. Warner, Nucl. Phys. B477 (1996) 746, hep-th/9604034.MathSciNetCrossRefGoogle Scholar
  39. [39]
    N. Seiberg and S. Shenker, Phys. Lett. B388 (1996) 521, hep-th/9608086.MathSciNetGoogle Scholar
  40. [40]
    A. Strominger, Nucl. Phys. B451 (1995) 96, hep-th/9504090.MathSciNetCrossRefGoogle Scholar
  41. [41]
    B. Greene, D. R. Morrison and A. Strominger, Nucl.Phys. B451 (1995) 109, hep-th/9504145.MathSciNetCrossRefGoogle Scholar
  42. [42]
    Articles in “Essays on Mirror Manifolds,” edited by S.-T. Yau, International Press, 1992.Google Scholar
  43. [43]
    M. Kontsevich, Proceedings of ICM, Zürich 1994, alg-geom/9411018.Google Scholar
  44. [44]
    A. Givental, alg-geom/9603021, alg-geom/9701016.Google Scholar
  45. [45]
    A. Strominger, S.-T. Yau and E. Zaslow, Nucl. Phys. B 479 (1996) 243, hep-th/9606040.MathSciNetCrossRefGoogle Scholar
  46. [46]
    D. R. Morrison, alg-geom/9608006.Google Scholar
  47. [47]
    M. Gross and P.M.H. Wilson, alg-geom/9608004.Google Scholar
  48. [48]
    C. Vafa and E. Witten, J. Geom. Phys. 15 (1995) 189, hep-th/9409188.MathSciNetMATHCrossRefGoogle Scholar
  49. [49]
    B. Greene, D. R. Morrison and C. Vafa, Nucl. Phys. B481 (1996) 513, hep-th/9608039.MathSciNetCrossRefGoogle Scholar
  50. [50]
    P. Candelas, P. S. Green and T. Hübsch, Phys. Rev. Lett. 62 (1989) 1956.MathSciNetCrossRefGoogle Scholar
  51. [51]
    M. Bershadsky and A. Johansen, Nucl. Phys. B489 (1997) 122.MathSciNetCrossRefGoogle Scholar
  52. [52]
    R. Friedman, J. Morgan and E. Witten, hep-th/9701162.Google Scholar
  53. [53]
    J.A. Minahan and D. Nemeschansky, Nucl. Phys. B489 (1997) 24, hep-th/9608047; Nucl. Phys. B482 (1996) 142, hep-th/9610076.MathSciNetCrossRefGoogle Scholar
  54. [54]
    O.J. Ganor, D.R. Morrison and N. Seiberg, Nucl. Phys. B487 (1997) 93, hep-th/9610251.MathSciNetCrossRefGoogle Scholar
  55. [55]
    W. Lerche, P. Mayr and N. Warner, hep-th/9612085.Google Scholar
  56. [56]
    E. Verlinde, Nucl. Phys. B455 (1995) 211, hep-th/9506011.MathSciNetCrossRefGoogle Scholar
  57. [57]
    E. Witten, hep-th/9703166.Google Scholar
  58. [58]
    S. Katz and D.R. Morrison, Journ. Alg. Geom. 1 (1992) 449.MathSciNetMATHGoogle Scholar
  59. [59]
    P.C. Argyres and A.D. Shapere, Nucl. Phys. B461 (1996) 437, hep-th/9509175.MathSciNetCrossRefGoogle Scholar
  60. [60]
    P.C. Argyres, M.R. Plesser and N. Seiberg, Nucl. Phys. B471 (1996) 159, hep-th/9603042.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Kentaro Hori
    • 1
    • 2
  • Hirosi Ooguri
    • 1
    • 2
  • Cumrun Vafa
    • 3
  1. 1.Department of PhysicsUniversity of California at BerkeleyBerkeleyUSA
  2. 2.Theoretical Physics GroupErnest Orlando Lawrence Berkeley National LaboratoryBerkeleyUSA
  3. 3.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

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