Skip to main content

Non-Perturbative Gauge Dynamics in Supersymmetric Theories. A Primer

  • Chapter
  • 618 Accesses

Part of the book series: NATO Science Series: B: ((NSSB,volume 368))

Abstract

I give an introductory review of recent, fascinating developments in supersymmetric gauge theories. I explain pedagogically the miraculous properties of supersymmetric gauge dynamics allowing one to obtain exact solutions in many instances. Various dynamical regimes emerging in supersymmetric Quantum Chromodynamics and its generalizations are discussed. I emphasize those features that have a chance of survival in QCD and those which are drastically different in supersymmetric and non-supersymmetric gauge theories. Unlike most of the recent reviews focusing almost entirely on the progress in extended supersymmetries (the Seiberg-Witten solution of N=2 models), these lectures are mainly devoted to N=1 theories. Developments “after Seiberg” (domain walls in supersymmetric gluodynamics) are briefly discussed.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Polyakov, Nucl. Phys. B120 (1977) 429.

    Article  ADS  MathSciNet  Google Scholar 

  2. S. Mandelstam, Phys. Reports 23 (1976) 245.

    Article  ADS  Google Scholar 

  3. G. ’t Hooft, in 1981 Cargése Summer School Lecture Notes on Fundamental Interactions, NATO Adv. Study Inst. Series B: Phys., Vol. 85, ed. M. Lévy et al. (Plenum Press, New York, 1982) [reprinted in G.’ t Hooft, Under the Spell of the Gauge Principle (World Scientific, Singapore, 1994), page 514]; Nucl. Phys. B190 (1981) 455.

    Google Scholar 

  4. Yu. Golfand and E. Likhtman, Pis’ma ZhETF, 13 (1971) 452 [JETP Lett. 13 (1971) 323]; see also in Problems of Theoretical Physics, I.E. Tamm Memorial Volume (Nauka, Moscow, 1972), page 37; E.P. Likhtman, Irreducible representations, extensions of the algebra of Poincaré. generators by bispinor generators, Kratk. Soob. Fiz. — Short Comm. Phys. FIAN, 1971, No. 5, page 197.

    ADS  Google Scholar 

  5. J. Wess and B. Zumino, Nucl. Phys. B70 (1974) 39; Phys. Lett. B49 (1974) 52.

    Article  ADS  MathSciNet  Google Scholar 

  6. W. Pauli, Pauli Lectures on Physics, Vol. 6, Selected Topics in Field Quantization (MIT Press, Cambridge, 1973), page 33.

    Google Scholar 

  7. A. Salam and J. Strathdee, Nucl. Phys. B76 (1974) 477; Phys. Rev. D11 (1975) 1521.

    Article  ADS  MathSciNet  Google Scholar 

  8. S. Ferrara and B. Zumino, Nucl. Phys. B79 (1974) 413.

    ADS  Google Scholar 

  9. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B229 (1983) 407.

    Article  ADS  Google Scholar 

  10. M. Shifman and A. Vainshtein, Nucl. Phys. B296 (1988) 445.

    Article  ADS  Google Scholar 

  11. A. Kovner and M. Shifman, Phys. Rev. D56 (1997) 2396.

    ADS  MathSciNet  Google Scholar 

  12. G. Veneziano and S. Yankielowicz, Phys. Lett. B113 (1982) 321; T. R. Taylor, G. Veneziano and S. Yankielowicz, Nucl. Phys. B218 (1983) 493.

    Google Scholar 

  13. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl.Phys. B229 (1983) 381; Phys. Lett. B166 (1986) 334.

    Article  ADS  Google Scholar 

  14. A. Salam and J. Strathdee, Nucl. Phys. B87 (1975) 85; P. Fayet, Nucl. Phys. B90 (1975) 104.

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Grisaru, in Recent Developments in Gravitation (Cargése Lectures, 1978), Eds. M. Levy and S. Deser (Plenum Press, New York, 1979), page 577, and references therein.

    Google Scholar 

  16. E. Witten, Nucl. Phys. B202 (1982) 253.

    Article  ADS  MathSciNet  Google Scholar 

  17. F. Buccella, J.-P. Derendinger, C. Savoy and S. Ferrara, Phys. Lett. B115 (1982) 375, and in Proc. Europhys. Study Conf. Unification of the Fundamental Particle Interactions. II, Eds. J. Ellis and S. Ferrara (Plenum Press, New York, 1983), page 349.

    ADS  MathSciNet  Google Scholar 

  18. I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B241 (1984) 493.

    Article  ADS  Google Scholar 

  19. I. Affleck, M. Dine and N. Seiberg, Nucl. Phys. B256 (1985) 557.

    Article  ADS  MathSciNet  Google Scholar 

  20. M. Luty and W. Taylor, Phys. Rev. D53 (1996) 3399.

    ADS  MathSciNet  Google Scholar 

  21. J. Bagger and J. Wess, Supersymmetry and Supergravity, 2nd Edition (Princeton University Press, Princeton, 1992).

    Google Scholar 

  22. E. Witten, Nucl. Phys. B403 (1993) 159.

    Article  ADS  MathSciNet  Google Scholar 

  23. A. Vainshtein, V. Zakharov and M. Shifman, Usp. Fiz. Nauk, 146 (1985) 683 [Sov. Phys.-. Usp. 28 (1985) 709].

    Article  MathSciNet  Google Scholar 

  24. I. Kogan, A. Morozov, M. Olshanetsky and M. Shifman, Yad. Fiz. 43 (1986) 1587 [Sov. J. Nucl. Phys. 43 (1986) 1022].

    Google Scholar 

  25. N. Seiberg, Phys. Rev. D49 (1994) 6857; Nucl. Phys. B435 (1995) 129.

    ADS  MathSciNet  Google Scholar 

  26. K. Intriligator and N. Seiberg, Nucl. Phys. B431 (1994) 551; K. Intriligator, R. Leigh, and N. Seiberg, Phys. Rev. D50 (1994) 1092.

    Article  ADS  MathSciNet  Google Scholar 

  27. K. Intriligator, R. Leigh, and M. Strassler, Nucl. Phys. B456 (1995) 567.

    Article  ADS  MathSciNet  Google Scholar 

  28. E. Poppitz and L. Randall, Phys. Lett. B336 (1994) 402; J. Bagger, E. Poppitz and L. Randall, Nucl. Phys. B426 (1994) 3.

    ADS  MathSciNet  Google Scholar 

  29. S. Giddings and J.M. Pierre, Phys. Rev. D52 (1995) 6065.

    ADS  MathSciNet  Google Scholar 

  30. T. Gherghetta, C. Kolda and S. Martin, Nucl. Phys. B468 (1996) 37.

    Article  ADS  MathSciNet  Google Scholar 

  31. J. Wess and B. Zumino, Phys. Lett. B49 (1974) 52; J. Iliopoulos and B. Zumino, Nucl. Phys. B76 (1974) 310; P. West, Nucl. Phys. B106 (1976) 219; M. Grisaru, M. Roček, and W. Siegel, Nucl. Phys. B159 (1979) 429.

    ADS  Google Scholar 

  32. Y. Meurice and G. Veneziano, Phys. Lett. B141 (1984) 69; I. Affleck, M. Dine and N. Seiberg, Phys. Lett. B137 (1984) 187.

    ADS  Google Scholar 

  33. D. Amati, K. Konishi, Y. Meurice, G. Rossi and G. Veneziano, Phys. Rep. 162 (1988) 557.

    Article  MathSciNet  Google Scholar 

  34. I. Affleck, M. Dine and N. Seiberg, Phys. Rev. Lett. 52 (1984) 1677; Y. Meurice and G. Veneziano, Phys. Lett. B141 (1984) 69.

    Article  ADS  Google Scholar 

  35. S. Ferrara and B. Zumino, Nucl. Phys. B87 (1975) 207.

    Article  ADS  Google Scholar 

  36. M. Shifman and A. Vainshtein, Nucl. Phys. B277 (1986) 456.

    Article  ADS  Google Scholar 

  37. I. Kogan, M. Shifman, and A. Vainshtein, Phys. Rev. D53 (1996) 4526.

    ADS  Google Scholar 

  38. J. Wess and B. Zumino, Phys. Lett. B49 (1974) 52.

    ADS  Google Scholar 

  39. M. Shifman and A. Vainshtein, Nucl. Phys. B359 (1991) 571.

    Article  ADS  MathSciNet  Google Scholar 

  40. I. Jack, D.R.T. Jones, and P. West, Phys. Lett. B258 (1991) 382.

    ADS  MathSciNet  Google Scholar 

  41. E. Poppitz and L. Randall, Phys. Lett. B389 (1996) 280.

    ADS  MathSciNet  Google Scholar 

  42. T.E. Clark, O. Piguet, and K. Sibold, Nucl. Phys. B159 (1979) 1; K. Konishi, Phys. Lett. B135 (1984) 439; K. Konishi and K. Shizuya, Nuov. Cim. A90 (1985) 111.

    Article  ADS  Google Scholar 

  43. V. Novikov, M. Shifman, A. Vainshtein and V. Zakharov, Nucl. Phys. B260 (1985) 157; for a review see23.

    Article  ADS  MathSciNet  Google Scholar 

  44. A. Vainshtein, V. Zakharov and M. Shifman, Yad. Fiz. 43 (1986) 1596 [Sov. J. Nucl. Phys. 43 (1986) 1028], Sect. 3; see also Pis’ma ZhETF 42 (1985) 182 [JETP Lett. 42 (1985) 224]; for a recent discussion see M. Shifman, Int. J. Mod. Phys. A11 (1996) 5761.

    Google Scholar 

  45. I. Jack, D.R.T. Jones and C.G. North, Nucl. Phys. B486 (1997) 479.

    Article  ADS  Google Scholar 

  46. N. Seiberg, Phys. Lett. 206B (1988) 75.

    ADS  MathSciNet  Google Scholar 

  47. N. Seiberg, Phys. Lett. B318 (1993) 469.

    ADS  MathSciNet  Google Scholar 

  48. I. Affleck, M. Dine and N. Seiberg, Phys. Rev. Lett. 51 (1983) 1026.

    Article  ADS  MathSciNet  Google Scholar 

  49. I. Affleck, M. Dine and N. Seiberg, Phys. Lett. B137 (1984) 187; Phys. Rev. Lett. 52 (1984) 493; Phys. Lett. B140 (1984) 59.

    ADS  Google Scholar 

  50. L. Dixon, V. Kaplunovsky and J. Louis, Nucl. Phys. B355 (1991) 649.

    Article  ADS  MathSciNet  Google Scholar 

  51. H. Li and K. Mahanthappa, Phys. Lett. B319 (1993) 152; Phys. Rev. D49 (1994) 5532.

    ADS  Google Scholar 

  52. M. Shifman (Ed.), Instantons in Gauge Theories (World Scientific, Singapore, 1994), Chapter VII.

    Google Scholar 

  53. B. Zumino, Phys. Lett. B69 (1977) 369.

    ADS  Google Scholar 

  54. A. D’Adda and P. Di Vecchia, Phys. Lett. B73 (1978) 162.

    Google Scholar 

  55. G.C. Rossi and G. Veneziano, Phys. Lett. B138 (1984) 195.

    ADS  Google Scholar 

  56. N. Seiberg and E. Witten, Nucl. Phys. B426 (1994) 19; (E) B430 (1994) 485; Nucl. Phys. B431 (1994) 484.

    Article  ADS  MathSciNet  Google Scholar 

  57. N. Dorey, V. Khoze, and M. Mattis, Phys. Rev, D54 (1996) 2921; Phys. Rev. D54 (1996) 7832; Phys. Lett. B388 (1996) 324; Phys. Lett. B390 (1997) 205; H. Aoyama, T. Harano, M. Sato, and S. Wada, Phys. Lett. B388 (1996) 331; K. Ito and N. Sasakura, Nucl. Phys. B484 (1997) 141; Mod. Phys. Lett. A12 (1997) 205; F. Fucito and T. Travaglini, Phys. Rev. D55 (1997) 1099; T. Harano and M. Sato, Nucl. Phys. B484 (1997) 167; Y. Yoshida, hep-th/9610211; M. Slater, Phys. Lett. B403 (1997) 57.

    ADS  MathSciNet  Google Scholar 

  58. A. Yung, Nucl. Phys. B485 (1997) 38.

    Article  ADS  MathSciNet  Google Scholar 

  59. S. Dimopoulos, Nucl. Phys. B168 (1980) 69; M. Peskin, Nucl. Phys. B175 (1980) 197.

    Article  ADS  MathSciNet  Google Scholar 

  60. M. Vysotsky, I. Kogan, and M. Shifman, Yad. Fiz. 42 (1985) 504 [Sov. J. Nucl. Phys. 42 (1985) 318].

    Google Scholar 

  61. A.C. Davis, M. Dine and N. Seiberg, Phys. Lett. B125 (1983) 487.

    ADS  Google Scholar 

  62. G. ’t Hooft, in Recent Developments in Gauge Theories, Eds. G. ’t Hooft et at., (Plenum Press, New York, 1980).

    Google Scholar 

  63. A. Dolgov and V. Zakharov, Nucl. Phys. B12 (1971) 68.

    Google Scholar 

  64. M. Shifman, Phys. Rep. 209 (1991) 161.

    Article  MathSciNet  Google Scholar 

  65. C. Vafa and E. Witten, Nucl. Phys. B234 (1984) 173.

    Article  ADS  MathSciNet  Google Scholar 

  66. S. Coleman and E. Witten, Phys. Rev. Lett. 45 (1980) 100.

    Article  ADS  MathSciNet  Google Scholar 

  67. E. Poppitz and S. Trivedi, Phys. Lett. B365 (1996) 125; P. Pouliot, Phys. Lett. B367 (1996) 151.

    ADS  MathSciNet  Google Scholar 

  68. K. Intriligator and P. Pouliot, Phys. Lett. B353 (1996) 471.

    ADS  MathSciNet  Google Scholar 

  69. P. Cho and P. Kraus, Phys. Rev. D54 (1996) 7640.

    ADS  MathSciNet  Google Scholar 

  70. C. Csáki, W. Skiba and M. Schmaltz, Nucl. Phys. B487 (1997) 128.

    Article  ADS  Google Scholar 

  71. K. Intriligator and N. Seiberg, Nucl. Phys. B444 (1995) 125.

    Article  ADS  MathSciNet  Google Scholar 

  72. P. Pouliot, Phys. Lett. B359 (1995) 108; P. Pouliot and M. Strassler, Phys. Lett. B370 (1996) 76; Phys. Lett. B375 (1996) 175.

    ADS  MathSciNet  Google Scholar 

  73. I. Pesando, Mod. Phys. Lett. A10 (1995) 1871; S. Giddings and J. Pierre, Phys. Rev. D52 (1995) 6065.

    MathSciNet  ADS  Google Scholar 

  74. C. Csáki, M. Schmaltz, and W. Skiba, Phys. Rev. Lett. 78 (1997) 799; Phys. Rev. D55 (1997) 7840.

    Article  ADS  Google Scholar 

  75. For a concise review and relevant references see e.g. I. Hinchliffe, Phys. Rev. D54 (1996) 77.

    Google Scholar 

  76. A. Belavin and A. Migdal, Pis’ma ZhETF 19 (1974) 317 [JETP Lett. 19 (1974) 181]; Scale. Invariance and Bootstrap in the Non-Abelian Gauge Theories, Landau Institute Preprint-74-0894, 1974 (unpublished).

    ADS  Google Scholar 

  77. T. Banks and Zaks, Nucl. Phys. B196 (1982) 189.

    Article  ADS  Google Scholar 

  78. N. Seiberg, Nucl. Phys. B435 (1995) 129.

    Article  ADS  MathSciNet  Google Scholar 

  79. D. Kutasov, A. Schwimmer, and N. Seiberg, Nucl. Phys. B459 (1996) 455.

    Article  ADS  MathSciNet  Google Scholar 

  80. G. ’t Hooft, Phys. Rev. D14 (1976) 3432; (E) D18 (1978) 2199.

    Google Scholar 

  81. P. Pouliot, Phys. Lett. B359 (1995) 108; D. Kutasov, Phys. Lett. B351 (1995) 230; D. Kutasov and A. Schwimmer, Phys. Lett. B354 (1995) 315; P. Pouliot and M. Strassler, Phys. Lett. B370 (1996) 76; B375 (1996) 175; K. Intriligator, Nucl. Phys. B448 (1995) 187; K. Intriligator, R. Leigh and M. Strassler, Nucl. Phys. B456 (1995) 567.

    ADS  MathSciNet  Google Scholar 

  82. J. Distler and A. Karch, hep-th/9611088.

    Google Scholar 

  83. J. Brodie and M. Strassler, hep-th/9611197; P. Cho, Phys. Rev. D56 (1997) 5260; and references therein.

    Google Scholar 

  84. G. Dvali and M. Shifman, Phys. Lett. B396 (1997) 64; (E) B407 (1997) 452.

    ADS  Google Scholar 

  85. R. Haag, J. Lopuszanski and M. Sohnius, Nucl. Phys. B88 (1975) 257.

    Article  ADS  MathSciNet  Google Scholar 

  86. S. Coleman and J. Mandula, Phys. Rev. 159 (1967) 1251.

    Article  ADS  MATH  Google Scholar 

  87. E. Witten and D. Olive, Phys. Lett. B78 (1978) 97.

    ADS  Google Scholar 

  88. S. Ferrara and B. Zumino, Nucl. Phys. B87 (1975) 207.

    Article  ADS  Google Scholar 

  89. B. Chibisov and M. Shifman, hep-th/9706089 [Phys. Rev. D, to appear).

    Google Scholar 

  90. E. Bogomol’nyi, Sov. J. Nucl. Phys. 24 (1976) 449, M.K. Prasad and C.H. Sommerfield, Phys. Rev. Lett. 35 (1976) 760.

    Google Scholar 

  91. G. Dvali and M. Shifman, hep-th/9611213 [Nucl. Phys. B, to appear].

    Google Scholar 

  92. M. Shifman, hep-th/9708060 [Phys. Rev. D, submitted]; M. Shifman and M. Voloshin, hep-th/9709137 [Phys. Rev. D, submitted].

    Google Scholar 

  93. A. Kovner, M. Shifman and A. Smilga, hep-th/9706089 [Phys. Rev. D, submitted]; A. Smilga and A. Veselov, hep-th/9710123.

    Google Scholar 

  94. E. Witten, hep-th/9706109.

    Google Scholar 

  95. V.B. Berestetskii, E.M, Lifshits and L.P. Pitaevskii, Quantum Electrodynamics, (Pergamon Press, New York, 1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Shifman, M. (2002). Non-Perturbative Gauge Dynamics in Supersymmetric Theories. A Primer. In: van Baal, P. (eds) Confinement, Duality, and Non-Perturbative Aspects of QCD. NATO Science Series: B:, vol 368. Springer, Boston, MA. https://doi.org/10.1007/0-306-47056-X_18

Download citation

  • DOI: https://doi.org/10.1007/0-306-47056-X_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-45826-2

  • Online ISBN: 978-0-306-47056-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics