Skip to main content
SpringerLink
Log in

Progress in Multi-Genus Calculations for the Spinning String

  • Chapter
Differential Geometric Methods in Theoretical Physics

Part of the book series: NATO ASI Series ((NSSB,volume 245))

  • 706 Accesses

Abstract

We review progress in the calculation of multiloop amplitudes for the closed Neveu-Schwarz-Ramond string in a flat ten dimensional background. When the picture changing operators are placed at the zeroes of a holomorphic one-form then it turns out to be possible to do the sum over spin structures for genus g ≤ 9 for the vacuum amplitude. The result of this sum is zero point wise in moduli space and not just a total derivative as might be expected in a more general gauge. We look at the possibility that singularities could arise for certain values of the moduli and also discuss why this gauge choice is so powerful by showing the similarity to “light-cone” diagrams.

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 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

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. J. H. Schwarz, Phys. Rep. 89C (1982), 223;

    Article  ADS  Google Scholar 

  2. J. Scherk, Rev. Mod. Phys. 47 (1975), 123;

    Article  MathSciNet  ADS  Google Scholar 

  3. E. D’Hoker and D. Phong, Rev. Mod. Phys. 60 (1988), 917.

    Article  MathSciNet  ADS  Google Scholar 

  4. J. H. Schwarz, ed., Superstrings, Vols. I and II, (World Scientific, Singapore, 1985);

    Google Scholar 

  5. M. B. Green and D. J. Gross, eds., Unified String Theories, (World Scientific, Singapore, 1986);

    MATH  Google Scholar 

  6. M. B. Green, J. H. Schwarz and E. Witten, Superstring Theory, Vols. I and II, (Cambridge University Press, 1987);

    MATH  Google Scholar 

  7. M. Kaku, Introduction to Superstrings, (Springer-Verlag, 1988).

    Book  MATH  Google Scholar 

  8. D. Friedan, E. Martinec and S. Shenker, Nucl. Phys. B271 (1986), 93.

    MathSciNet  ADS  Google Scholar 

  9. E. Martinec, Nuci Phys. B281 (1986), 157.

    MathSciNet  ADS  Google Scholar 

  10. E. Verlinde and H. Verlinde, Phys. Lett. B192 (1987), 95.

    MathSciNet  ADS  Google Scholar 

  11. J.J. Atick, J. Rabin and A. Sen, Nucl. Phys. B299 (1988), 279.

    Article  MathSciNet  ADS  Google Scholar 

  12. J.J. Atick, G. Moore and A. Sen, Nucl. Phys. B307 (1988), 221.

    Article  MathSciNet  ADS  Google Scholar 

  13. J.J. Atick, G. Moore and A. Sen, Nucl. Phys. B308 (1988), 1.

    MathSciNet  ADS  Google Scholar 

  14. G. Moore and A. Morozov, Nucl. Phys. B306 (1988), 387.

    Article  MathSciNet  ADS  Google Scholar 

  15. H. La and P. Nelson, “Unambiguous fermionic string amplitudes”, BUHEP-89–8,UPR-0381T, Feb 89.

    Google Scholar 

  16. M. Martellini and P. Teofilatto, Phys. Lett. B211 (1988), 293.

    MathSciNet  ADS  Google Scholar 

  17. A. Parkes, Phys. Lett. B217 (1989), 458.

    MathSciNet  ADS  Google Scholar 

  18. O. Lechtenfeld and A. Parkes, Nucl. Phys. B.to be published. “On covariant multi-loop superstring amplitudes” April 1989.

    Google Scholar 

  19. D. Mumford, Tata Lectures on Theta,, Birkhäuser, Boston 1983.

    MATH  Google Scholar 

  20. J. Fay, Theta, Functions on Riemann Surfaces, Springer Notes in Mathematics 352, 1973.

    Google Scholar 

  21. H.M. Farkas and I. Kra, Riemann Surfaces (Springer, 1980).

    Book  Google Scholar 

  22. G. Moore, P. Nelson and J. Polchinski, Phys. Lett. B169 (1986), 47;

    MathSciNet  ADS  Google Scholar 

  23. G. Moore and P. Nelson, Nucl. Phys. B274 (1986), 509;

    MathSciNet  ADS  Google Scholar 

  24. E. D’Hoker and D. Phong, Nucl. Phys. B278 (1986), 225,

    Article  MathSciNet  ADS  Google Scholar 

  25. E. D’Hoker and D. Phong, Nucl. Phys.ibid. B292 (1987), 317;

    Article  MathSciNet  ADS  Google Scholar 

  26. S. Chaudhuri, H. Kawai and S.-H. Tye, Cornell preprint CLNS 86/723 (1986).

    Google Scholar 

  27. E. Verlinde and H. Verlinde, Nucl. Phys. B288 (1987), 357.

    Article  MathSciNet  ADS  Google Scholar 

  28. O. Lechtenfeld and A. Parkes, Phys. Lett. B202 (1988), 75.

    MathSciNet  ADS  Google Scholar 

  29. O. Lechtenfeld, “Superconformai ghost correlations on Riemann surfaces”, City College preprint CCNY-HEP-89/09.

    Google Scholar 

  30. A. Tsuchiya, Phys. Rev. D39 (1989), 1626, “On the non-renormalization theorem in superstring theories at the two loop order”, TIT-HEP April, 1989.

    MathSciNet  ADS  Google Scholar 

  31. A. Morozov, Nucl. Phys. B318 (1989), 137;

    Article  ADS  Google Scholar 

  32. A. Morozov and A. Perelomov, Int. J. Mod. Phys. A4 (1989), 1773

    MathSciNet  ADS  Google Scholar 

  33. A. Morozov, Nucl. Phys. B303 (1988), 343.

    Article  ADS  Google Scholar 

  34. O. Lechtenfeld, Nucl. Phys. B309 (1988) 361, “On the finiteness of the super-string” Nucl. Phys. B to be published.

    MathSciNet  ADS  Google Scholar 

  35. L. Dixon, D. Friedan, E. Martinec and S.H. Shenker, Nucl. Phys. B282 (1987) 13;

    Article  MathSciNet  ADS  Google Scholar 

  36. A.B. Zamolodchikov, Nucl. Phys. B285 (1987) 481;

    Article  MathSciNet  ADS  Google Scholar 

  37. M. Bershadsky and A. Radul, Int. J. Mod. Phys. A2 (1987) 165;

    MathSciNet  ADS  Google Scholar 

  38. V. Knizhnik, Comm. Math. Phys. 112 (1987) 567,

    Article  MathSciNet  ADS  MATH  Google Scholar 

  39. V. Knizhnik, Phys. Lett. B196 (1987) 473;

    MathSciNet  ADS  Google Scholar 

  40. D. Montano, Nucl. Phys. B297 (1987) 125;

    MathSciNet  ADS  Google Scholar 

  41. D. Lebedev and A. Morozov, Nucl. Phys. B302 (1988) 163.

    Article  MathSciNet  ADS  Google Scholar 

  42. E. Gava, R. Iengo and G. Sotkov, Phys. Lett. B207 (1988) 283

    MathSciNet  ADS  Google Scholar 

  43. R. Iengo and C.-J. Zhu, Phys. Lett. B212 (1988) 309, 313

    ADS  Google Scholar 

  44. C.-J. Zhu, Trieste preprint ISAS/88/147 (1988).

    Google Scholar 

  45. M. Bershadsky, Phys. Lett. B201 (1988) 67.

    MathSciNet  ADS  Google Scholar 

  46. S.B. Giddings and S.A. Wolpert, Comm. Math. Phys. 109 (1987) 177;

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. E. D’Hoker and S.B. Giddings, Nucl. Phys. B291 (1987) 90;

    Article  MathSciNet  ADS  Google Scholar 

  48. N. Berkovits, Nucl. Phys. B304 (1988) 537,

    Article  MathSciNet  ADS  Google Scholar 

  49. N. Berkovits, Phys. Lett. B219 (1989) 278;

    MathSciNet  ADS  Google Scholar 

  50. R. Tzani, Phys. Rev. D15 (1988) 3112, “The problem of the gauge in Polyakov’s theory: Relation between light-cone and conformai gauge” City College preprint CCNY-HEP-89/1.

    ADS  Google Scholar 

  51. K.-J. Hamada and M. Takao, Int. J. Mod. Phys. A4 (1989) 2283,

    MathSciNet  ADS  Google Scholar 

  52. K.-J. Hamada and M. Takao, Nucl. Phys. B313 (1989) 80.

    Article  MathSciNet  ADS  Google Scholar 

  53. E. D’Hoker and D.H. Phong “Functional determinants on mandelstam diagrams”, Preprint UCLA/88/TEP/39.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, University of California, Davis, CA, 95616, USA

    Andrew Parkes

Authors
  1. Andrew Parkes
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Davis, Davis, California, USA

    Ling-Lie Chau  & Werner Nahm  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer Science+Business Media New York

About this chapter

Cite this chapter

Parkes, A. (1990). Progress in Multi-Genus Calculations for the Spinning String. In: Chau, LL., Nahm, W. (eds) Differential Geometric Methods in Theoretical Physics. NATO ASI Series, vol 245. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-9148-7_45

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-9148-7_45

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-9150-0

  • Online ISBN: 978-1-4684-9148-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation