Skip to main content
SpringerLink
Log in

From dual amplitudes to non-critical strings: a brief review

  • Published:
La Rivista del Nuovo Cimento (1978-1999) Aims and scope

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.

Institutional subscriptions

References

  1. R. Dolen, D. Horn andC. Schmid:Phys. Rev. Lett.,19 (1967);Phys. Rev.,166, 1768 (1968).

    Google Scholar 

  2. Y. Nambu:Proceedings of the International Conference on Symmetries and Quark Models (1969) Wayne:Lectures at Copenhagen Symposium (1970).

  3. H. B. Nielsen:Proceedings of the XV International Conference on High Energy Physics, Kiev, 1970.

  4. L. Susskind:Nuovo Cimento A,69, 457 (1970).

    MathSciNet  ADS  Google Scholar 

  5. P. Ramond:Phys. Rev. D,3, 2415 (1971).

    MathSciNet  ADS  Google Scholar 

  6. J. Scherk:Rev. Mod. Phys.,47, 123 (1975).

    MathSciNet  ADS  Google Scholar 

  7. J. Scherk andJ. H. Schwarz:Nucl. Phys. B,81, 118 (1974);Phys. Lett. B,57, 463 (1975).

    ADS  Google Scholar 

  8. M. B. Green andJ. H. Schwarz:Phys. Lett. B,136, 367 (1984);Nucl. Phys. B,243, 285 (1984).

    ADS  Google Scholar 

  9. A. A. Belavin, A. M. Polyakov andA. B. Zamolodchikov:Nucl. Phys. B,241, 333 (1984).

    MathSciNet  ADS  MATH  Google Scholar 

  10. P. Ginsparg: inProceedings Les Houches 1988, edited byE. Brézin andJ. Zinn-Justin (Elsevier, Amsterdam, 1989).

    Google Scholar 

  11. L. Alvarez-Gaumé, C. Gómez andG. Sierra: inPhysics and Mathematics of Strings, Memorial Volume for Vadim Knizhnik, edited byL. Brink, D. Friedan andA. M. Polyakov (World Scientific, Singapore, 1980).

    Google Scholar 

  12. L. Alvarez-Gaumé:Random Surfaces, Statistical Mechanics and String Theory, Troisième Cycle de la Physique en Suisse Romande, Sémestre d’Hiver 1990;Helv. Phys. Acta, 1 (1991).

  13. A. Pressley andG. Segal:Loop Groups (Oxford University Press, New York, 1986).

    MATH  Google Scholar 

  14. V. Kac:Infinite-dimensional Lie algebras (Birkhäuser, Basel, 1983).

    MATH  Google Scholar 

  15. H. Farkas andI. Kra:Riemann Surfaces (Springer, Heidelberg, 1984).

    Google Scholar 

  16. P. Griffiths andJ. Harris:Principles of Algebraic Geometry (Wiley, New York, 1978).

    MATH  Google Scholar 

  17. C. Gómez, M. Ruiz-Altaba andG. Sierra:Quantum Groups in Two-dimensional Physics (Cambridge University Press, New York, 1993).

    Google Scholar 

  18. L. Kauffmann:Knot Theory (World Scientific, Singapore, 1991).

    Google Scholar 

  19. G. Veneziano:Nuovo Cimento A,57, 190 (1968).

    ADS  Google Scholar 

  20. M. A. Virasoro:Phys. Rev.,177, 2309 (1969).

    MathSciNet  ADS  Google Scholar 

  21. J. Shapiro:Phys. Lett. B,33, 361 (1970).

    ADS  Google Scholar 

  22. K. Bardakci andH. Ruegg:Phys. Lett. B,28, 485 (1969).

    Google Scholar 

  23. K. Bardakci andH. Ruegg:Phys. Rev.,181, 1884 (1969).

    ADS  Google Scholar 

  24. M. Virasoro:Phys. Rev. D,1, 2933 (1970).

    ADS  Google Scholar 

  25. S. Fubini andG. Veneziano:Nuovo Cimento A,64, 811 (1969);67, 29 (1970).

    ADS  Google Scholar 

  26. P. Goddard, J. Goldstone, C. Rebbi andC. B. Thorn:Nucl. Phys. B,56, 109 (1973).

    ADS  Google Scholar 

  27. E. Del Giudice, P. Di Vecchia andS. Fubini:Ann. Phys.,70, 378 (1972).

    ADS  Google Scholar 

  28. G. Veneziano:Phys. Rep. C,9, 199 (1974).

    ADS  Google Scholar 

  29. V. Alessandrini, D. Amati, M. Le Bellac andD. Olive:Phys. Rep. C,1 269 (1971).

    ADS  Google Scholar 

  30. J. H. Schwarz:Phys. Rep. C,8, 269 (1973).

    ADS  Google Scholar 

  31. C. Rebbi:Phys. Rep. C,12, 1 (1974).

    MathSciNet  ADS  Google Scholar 

  32. S. Mandelstam:Phys. Rep. C,13, 261 (1974).

    ADS  Google Scholar 

  33. M. Jacob (Editor):Dual Theory (North-Holland, Amsterdam and Oxford, 1974).

    Google Scholar 

  34. L. Alvarez-Gaumé, C. Gómez, G. Moore andC. Vafa:Nucl. Phys. B,303, 455 (1988).

    ADS  Google Scholar 

  35. L. Alvarez-Gaumé, C. Gómez, P. Nelson, G. Sierra andC. Vafa:Nucl. Phys. B,311, 333 (1988).

    ADS  Google Scholar 

  36. A. Polyakov:Phys. Lett. B,103, 207 (1981).

    MathSciNet  ADS  Google Scholar 

  37. D. Friedan: inProceedings Les Houches 1982, edited byR. Stora andJ. B. Zuber (North-Holland, Amsterdam, 1983);Ann. Phys.,163, 318 (1985).

    Google Scholar 

  38. M. Peskin:Proceedings TASI 1986, edited byH. Haber (World Scientific, Singapore, 1987).

    Google Scholar 

  39. M. Green, J. Schwarz andE. Witten:Superstring Theory, 2 vols. (Cambridge University Press, 1986).

  40. Encyclopedic Dictionary of Mathematics, English translation (MIT Press, Boston, 1981).

  41. Soviet Dictionary of Mathematics (Mir, Moskva, 1986).

  42. M. A. Virasoro:Phys. Rev. Lett.,22, 37 (1969).

    ADS  Google Scholar 

  43. H. M. Chan andS. T. Tsou:Phys. Lett. B,28, 485 (1969).

    ADS  Google Scholar 

  44. C. G. Goebel andB. Sakita:Phys. Rev. Lett.,22, 257 (1969).

    ADS  Google Scholar 

  45. Z. Koba andH. B. Nielsen:Nucl. Phys. B,10, 633 (1969).

    ADS  Google Scholar 

  46. Z. Koba andH. B. Nielsen:Nucl. Phys. B,12, 517 (1969).

    ADS  Google Scholar 

  47. S. Fubini, D. Gordon andG. Veneziano:Phys. Lett. B,29, 679 (1969).

    ADS  Google Scholar 

  48. C. Lovelace:Phys. Lett. B,32, 490 (1970).

    MathSciNet  ADS  Google Scholar 

  49. R. C. Brower andC. B. Thorn:Nucl. Phys. B,31, 163 (1971).

    MathSciNet  ADS  Google Scholar 

  50. C. B. Thorn:Nucl. Phys. B,248, 551 (1984).

    MathSciNet  ADS  Google Scholar 

  51. L. Brink andH. B. Nielsen:Phys. Lett. B.,4, 332 (1973).

    ADS  Google Scholar 

  52. L. Alvarez-Gaumé, C. Gómez andC. Reina:Phys. Lett. B.,190, 55 (1987).

    MathSciNet  ADS  Google Scholar 

  53. G. Segal andG. Wilson:Publ. Math. IHES,61, 5 (1985).

    MathSciNet  MATH  Google Scholar 

  54. V. G. Kac andD. H. Peterson:Adv. Math.,53, 125 (1984).

    MathSciNet  MATH  Google Scholar 

  55. I. Frenkel: inLect. Appl. Math.,21, 325 (1985).

    Google Scholar 

  56. L. Alvarez-Gaumé, J. B. Bost, G. Moore, P. Nelson andC. Vafa:Comm. Math. Phys.,112, 503 (1987).

    MathSciNet  ADS  MATH  Google Scholar 

  57. B. L. Feigin:Usp. Mat. Nauk,39, 195 (1984).

    MathSciNet  MATH  Google Scholar 

  58. M. Sato:RIMS Kokyuroku,439, 30 (1981).

    Google Scholar 

  59. M. Sato, T. Miwa andM. Jimbo:Publ. RIMS Kyoto Univ. 15, 201 (1979).

    MathSciNet  MATH  Google Scholar 

  60. K. Kikkawa, B. Sakita andM. A. Virasoro:Phys. Rev.,184, 1701 (1969).

    MathSciNet  ADS  Google Scholar 

  61. D. Friedan andS. Shenker:Nucl. Phys. B,281, 509 (1987).

    MathSciNet  ADS  Google Scholar 

  62. D. Friedan, E. Martinec andS. Shenker:Nucl. Phys. B,271, 93 (1986).

    MathSciNet  ADS  Google Scholar 

  63. E. Verlinde andH. Verlinde:Nucl. Phys. B,288, 357 (1988).

    MathSciNet  ADS  Google Scholar 

  64. Yu. I. Manin andA. O. Radul:Comm. Math. Phys.,98, 65 (1985).

    MathSciNet  ADS  MATH  Google Scholar 

  65. D. G. Quillen:Funk. Anal. Pril,19, 37 (1985).

    MathSciNet  Google Scholar 

  66. J. Smit: Doctoral Thesis, Utrecht (1987).

  67. L. Brink, P. di Vecchia andP. Howe:Phys. Lett. B,65, 471 (1976);S. Deser andB. Zumino:Phys. Lett. B,65, 393 (1976).

    ADS  Google Scholar 

  68. D. Gross, J. Harvey, E. Martinec andR. Rohm:Nucl. Phys. B,256, 253 (1985);267, 75 (1985).

    MathSciNet  ADS  Google Scholar 

  69. I. Frenkel, H. Garland andG. Zuckerman:Proc. Nat. Acad. Sci. US,83, 8442 (1986).

    MathSciNet  ADS  MATH  Google Scholar 

  70. T. Banks andM. Peskin:Nucl. Phys. B,264, 513 (1986).

    MathSciNet  ADS  Google Scholar 

  71. C. Lovelace:Phys. Lett. B,135, 207, 211 (1981).

    MathSciNet  Google Scholar 

  72. E. S. Fradkin andA. A. Tseytlin:Nucl. Phys. B,261, 1 (1985).

    MathSciNet  ADS  Google Scholar 

  73. C. Callan, D. Friedan, E. Martinec andM. Perry:Nucl. Phys. B,262, 593 (1985).

    MathSciNet  ADS  Google Scholar 

  74. A. Sen:Phys. Rev. D,32, 2102 (1985);Phys. Rev. Lett.,55, 1846 (1985).

    ADS  Google Scholar 

  75. A. B. Zamolodchikov:JETP Lett.,46, 160 (1987).

    MathSciNet  ADS  Google Scholar 

  76. B. Zwiebach:Nucl. Phys. B,390, 33 (1993).

    MathSciNet  ADS  Google Scholar 

  77. B. L. Feigin andD. B. Fuks:Funkt. Anal. Prilozhen.,16, 47 (1982); Moscow preprint (1983).

    MathSciNet  Google Scholar 

  78. V. S. Dotsenko andV. A. Fateev:Nucl. Phys. B,240, 312 (1984);251, 691 (1985).

    MathSciNet  ADS  Google Scholar 

  79. A. Rocha-Caridi: inVertex Operators in Mathematics and Physics, edited byJ. Lepowsky, S. Mandelstam andI. M. Singer (Publ. #3, Springer, New York, 1984); inProceedings X Johns Hopkins, edited byV. Rittenberg (World Scientific, Singapore, 1986).

    Google Scholar 

  80. B. Lian andG. Zuckerman:Phys. Lett. B,254, 417 (1990).

    MathSciNet  ADS  Google Scholar 

  81. P. Bouwknegt, J. McCarty andK. Pilch:Commun. Math. Phys.,145, 541 (1992).

    ADS  MATH  Google Scholar 

  82. M. Goulian andM. Li:Phys. Rev. Lett.,66, 2051 (1991).

    ADS  Google Scholar 

  83. V. S. Dotsenko:Mod. Phys. Lett. A,6, 3601 (1991).

    MathSciNet  ADS  MATH  Google Scholar 

  84. Y. Kitazawa:Phys. Lett. B,265, 262 (1991).

    MathSciNet  ADS  Google Scholar 

  85. P. Di Francesco andD. Kutrasov:Nucl. Phys. B,342, 589 (1990).

    ADS  Google Scholar 

  86. L. Alvarez-Gaumé, J. L. F. Barbón andC. Gómez:Nucl. Phys. B,368, 57 (1992).

    ADS  Google Scholar 

  87. V. S. Dotsenko andV. A. Fateev:Phys. Lett. B,154, 291 (1985).

    MathSciNet  ADS  Google Scholar 

  88. E. Verlinde:Nucl. Phys. B,300, 360 (1988).

    MathSciNet  ADS  MATH  Google Scholar 

  89. J. Polchinski:Nucl. Phys. B,357, 241 (1991).

    MathSciNet  ADS  Google Scholar 

  90. A. M. Polyakov:Mod. Phys. Lett. A,6, 635 (1990).

    MathSciNet  ADS  Google Scholar 

  91. D. J. Gross andI. Klebanov:Nucl. Phys. B,359, 3 (1991).

    MathSciNet  ADS  MATH  Google Scholar 

  92. V. G. Knizhnik, A. M. Polyakov andA. B. Zamolodchikov:Mod. Phys. Lett. A,3, 819 (1988).

    MathSciNet  ADS  Google Scholar 

  93. E. Brezin andV. Kazakov:Phys. Lett. B,236, 144;M. Douglas andS. Shenker:Nucl. Phys. B,335, 635 (1990);D. J. Gross andA. A. Midgal:Phys. Rev. Lett.,64, 717 (1990).

    Google Scholar 

  94. J. Distler andH. Kawai:Nucl. Phys. B,321, 509 (1989).

    MathSciNet  ADS  Google Scholar 

  95. F. David:Mod. Phys. Lett. A,3, 1651 (1988).

    ADS  Google Scholar 

  96. K. Fujikawa:Phys. Rev. D,25, 2584 (1982).

    ADS  Google Scholar 

  97. C. Becchi, A. Rouet andR. Stora:Ann. Phys. (N.Y.),98, 287 (1976).

    MathSciNet  ADS  Google Scholar 

  98. E. S. Fradkin andG. Vilkovisky:Phys. Lett. B,55, 224 (1975);I.A. Batalina andG. Vilkovisky:Phys. Lett. B,69, 309 (1977);E. S. Fradkin andT. E. Fradkina:Phys. Lett. B,72, 343 (1978).

    MathSciNet  ADS  MATH  Google Scholar 

  99. T. Kugo andI. Ojima:Phys. Lett. B,73, 459 (1978).

    ADS  Google Scholar 

  100. M. Henneaux:Phys. Rep. C,126, 1 (1985).

    MathSciNet  ADS  Google Scholar 

  101. J. A. Hempel:Bull. London Math. Soc.,20, 97 (1988).

    MathSciNet  MATH  Google Scholar 

  102. P. G. Zograf andL. A. Takhtadjan:Matem. Sbornik,132, 174 (1987); translated inMath. USSR Sbornik,60, 297 (1988).

    Google Scholar 

  103. E. L. Ince:Ordinary Differential Equations (Dover, New York, N.Y., 1956; reprint from 1926).

    Google Scholar 

  104. C. Gómez andG. Sierra:Phys. Lett. B,255, 51 (1991).

    MathSciNet  ADS  Google Scholar 

  105. T. Curtright andC. B. Thorn:Phys. Rev. Lett.,48, 1309 (1982);E. Braaten, T. Curtright andC. B. Thorn:Phys. Lett. B,118, 115 (1982);Ann. Phys.,147, 356 (1983);E. Braaten, T. Curtright, G. Ghandour andC. B. Thorn:Phys. Rev. Lett.,51, 19 (1983);Ann. Phys.,153, 147 (1984).

    MathSciNet  ADS  Google Scholar 

  106. J. L. Gervais andA. Neveu:Nucl. Phys. B,199, 59 (1982);209, 125 (1982);224, 329 (1983);238, 125, 396 (1984);Phys. Lett. B,151, 271 (1985).

    MathSciNet  ADS  Google Scholar 

  107. J. L. Gervais:Commun. Math. Phys.,130, 257 (1990).

    MathSciNet  ADS  MATH  Google Scholar 

  108. N. Seiberg:Notes on Quantum Liouville Theory and Quantum Gravity, New Jersey preprint RU-90-29 presented at the 1990 Yukawa International Seminar, Kyoto.

  109. F. Smirnov andL. Takhtadjan: Colorado preprint (1990), unpublished.

  110. M. Fukuma, R. Kawai andR. Nakayama:Int. J. Mod. Phys. A,6, 1385 (1991).

    MathSciNet  ADS  Google Scholar 

  111. R. Dijkgraaf, E. Verlinde andH. Verlinde:Nucl. Phys. B,348, 435 (1991).

    MathSciNet  ADS  Google Scholar 

  112. E. Witten:Nucl Phys. B,340, 281 (1990);R. Dijkgraaf andE. Witten:Nucl. Phys. B,342, 486 (1990).

    ADS  Google Scholar 

  113. G. Moore, N. Seiberg andM. Staudacher:Nucl. Phys. B,362, 665 (1991).

    MathSciNet  ADS  Google Scholar 

  114. M. Bershadsky andI. Klebanov:Nucl. Phys. B,360, 559 (1991).

    MathSciNet  ADS  Google Scholar 

  115. P. Di Francesco andD. Kutasov:Phys. Lett. B,261, 385 (1991).

    MathSciNet  ADS  Google Scholar 

  116. A. Gupta, S. P. Trivedi andM. B. Wise:Nucl. Phys. B,340, 475 (1990).

    MathSciNet  ADS  Google Scholar 

  117. E. Martinec, G. Moore andN. Seiberg:Phys. Lett. B,263, 190 (1991).

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department de Physique Théorique, Université de Genève, CH-1211, Genève 4

    C. Gomez

  2. Instituto de Física Fundamental CSIC, Serrano 123, 28006, Madrid

    C. Gomez & M. Ruiz-Altaba

Authors
  1. C. Gomez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Ruiz-Altaba
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work supported in part by the Fonds National Suisse de la Recherche Scientifique.

These notes are partly based on eight lectures given by C. Gómez as a «Cours de Troisième Cycle de la Physique en Suisse Romande» during spring 1991 in Lausanne.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gomez, C., Ruiz-Altaba, M. From dual amplitudes to non-critical strings: a brief review. Riv. Nuovo Cim. 16, 1–124 (1993). https://doi.org/10.1007/BF02728245

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02728245

Search

Navigation