Skip to main content
SpringerLink
Log in

Multiloop amplitudes of light-cone gauge bosonic string field theory in noncritical dimensions

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We study the multiloop amplitudes of the light-cone gauge closed bosonic string field theory for d ≠ 26. We show that the amplitudes can be recast into a BRST invariant form by adding a nonstandard worldsheet theory for the longitudinal variables X ± andthereparametrizationghostsystem. Theresultsobtainedinthispaperforbosonic strings provide a first step towards the examination whether the dimensional regularization works for the multiloop amplitudes of the light-cone gauge superstring field theory.

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

Similar content being viewed by others

References

  1. M. Kaku and K. Kikkawa, The Field Theory of Relativistic Strings, Pt. 1. Trees, Phys. Rev. D 10 (1974) 1110 [INSPIRE].

    ADS  Google Scholar 

  2. M. Kaku and K. Kikkawa, The Field Theory of Relativistic Strings. 2. Loops and Pomerons, Phys. Rev. D 10 (1974) 1823 [INSPIRE].

    ADS  Google Scholar 

  3. S. Mandelstam, Interacting String Picture of Dual Resonance Models, Nucl. Phys. B 64 (1973) 205 [INSPIRE].

    Article  ADS  Google Scholar 

  4. E. Cremmer and J.-L. Gervais, Infinite Component Field Theory of Interacting Relativistic Strings and Dual Theory, Nucl. Phys. B 90 (1975) 410 [INSPIRE].

    Article  ADS  Google Scholar 

  5. J. Greensite and F.R. Klinkhamer, New interactions for superstrings, Nucl. Phys. B 281 (1987) 269 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. J. Greensite and F.R. Klinkhamer, Contact interactions in closed superstring field theory, Nucl. Phys. B 291 (1987) 557 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. M.B. Green and N. Seiberg, Contact interactions in superstring theory, Nucl. Phys. B 299 (1988) 559 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. J. Greensite and F.R. Klinkhamer, Superstring amplitudes and contact interactions, Nucl. Phys. B 304 (1988) 108 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. C. Wendt, Scattering amplitudes and contact interactions in Witten’s superstring field theory, Nucl. Phys. B 314 (1989) 209 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. Y. Baba, N. Ishibashi and K. Murakami, Light-Cone Gauge Superstring Field Theory and Dimensional Regularization, JHEP 10 (2009) 035 [arXiv:0906.3577] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. Y. Baba, N. Ishibashi and K. Murakami, Light-Cone Gauge String Field Theory in Noncritical Dimensions, JHEP 12 (2009) 010 [arXiv:0909.4675] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. Y. Baba, N. Ishibashi and K. Murakami, Light-cone Gauge Superstring Field Theory and Dimensional Regularization II, JHEP 08 (2010) 102 [arXiv:0912.4811] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. Y. Baba, N. Ishibashi and K. Murakami, Light-cone Gauge NSR Strings in Noncritical Dimensions, JHEP 01 (2010) 119 [arXiv:0911.3704] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  14. N. Ishibashi and K. Murakami, Light-cone Gauge NSR Strings in Noncritical Dimensions II — Ramond Sector, JHEP 01 (2011) 008 [arXiv:1011.0112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. N. Ishibashi and K. Murakami, Spacetime Fermions in Light-cone Gauge Superstring Field Theory and Dimensional Regularization, JHEP 07 (2011) 090 [arXiv:1103.2220] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. S.B. Giddings and S.A. Wolpert, A triangulation of moduli space from light-cone string theory, Commun. Math. Phys. 109 (1987) 177 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. E. D’Hoker and D. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. J.D. Fay, Theta Functions on Riemann Surfaces, Lecture Notes in Mathematics. Vol. 352., Springer-Verlag, (1973).

  19. D. Mumford, Tata Lectures on Theta II, Birkhauser Boston, (1984).

  20. E. D’Hoker and S.B. Giddings, Unitary of the closed bosonic Polyakov string, Nucl. Phys. B 291 (1987) 90 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. H. Sonoda, Functional determinants on punctured Riemann surfaces and their application to string THEORY, Nucl. Phys. B 294 (1987) 157 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. E. D’Hoker and D. Phong, Functional determinants on Mandelstam diagrams, Commun. Math. Phys. 124 (1989) 629 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. S. Mandelstam, The interacting string picture and functional integration, Lectures given at Workshop on Unified String Theories, Santa Barbara, CA, U.S.A., July 29 - August 16 (1985).

  24. T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys. 87 (1992) 801 [hep-th/9201040] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. H. Hata, K. Itoh, T. Kugo, H. Kunitomo and K. Ogawa, Covariant String Field Theory, Phys. Rev. D 34 (1986) 2360 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  26. H. Hata, K. Itoh, T. Kugo, H. Kunitomo and K. Ogawa, Covariant String Field Theory. II, Phys. Rev. D 35 (1987) 1318 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  27. N. Berkovits, Calculation of scattering amplitudes for the Neveu-Schwarz model using supersheet functional integration, Nucl. Phys. B 276 (1986) 650 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. N. Berkovits, Supersheet functional integration and the interacting Neveu-Schwarz string, Nucl. Phys. B 304 (1988) 537 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. N. Berkovits, Supersheet functional integration and the calculation of NSR scattering amplitudes involving arbitrarily many external Ramond strings, Nucl. Phys. B 331 (1990) 659 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. K. Aoki, E. D’Hoker and D. Phong, Unitarity of closed superstring perturbation theory, Nucl. Phys. B 342 (1990) 149 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].

  32. E. Witten, More On Superstring Perturbation Theory, arXiv:1304.2832 [INSPIRE].

  33. E. Witten, Notes On Supermanifolds and Integration, arXiv:1209.2199 [INSPIRE].

  34. E. Witten, Notes On Super Riemann Surfaces And Their Moduli, arXiv:1209.2459 [INSPIRE].

  35. M.J. Dugan and H. Sonoda, Functional determinants on Riemann surfaces, Nucl. Phys. B 289 (1987) 227 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. A. LeClair, M.E. Peskin and C. Preitschopf, String Field Theory on the Conformal Plane. II. Generalized Gluing, Nucl. Phys. B 317 (1989) 464 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. A. Sen, Open string field theory in nontrivial background field: gauge invariant action, Nucl. Phys. B 334 (1990) 350 [INSPIRE].

    Article  ADS  Google Scholar 

  38. L. Rastelli and B. Zwiebach, Tachyon potentials, star products and universality, JHEP 09 (2001) 038 [hep-th/0006240] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. M. Schnabl, Wedge states in string field theory, JHEP 01 (2003) 004 [hep-th/0201095] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. L. Álvarez-Gaumé, J. Bost, G.W. Moore, P.C. Nelson and C. Vafa, Bosonization on Higher Genus Riemann Surfaces, Commun. Math. Phys. 112 (1987) 503 [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  41. E.P. Verlinde and H.L. Verlinde, Chiral Bosonization, Determinants and the String Partition Function, Nucl. Phys. B 288 (1987) 357 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. G. Faltings, Calculus on arithmetic surfaces, Ann. Math. 119 (1984) 387.

    Article  MathSciNet  MATH  Google Scholar 

  43. R. Wentworth, The asymptotics of the Arakelov-Green’s function and Faltings’ delta invariant, Commun. Math. Phys. 137 (1991) 427.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. A. Yamada, Precise variational formulas for abelian differentials, Kodai. Math. J. 3 (1980) 114.

    Article  MathSciNet  MATH  Google Scholar 

  45. J. Igusa, Theta Functions, Springer-Verlag, (1972).

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, University of Tsukuba, Tsukuba, Ibaraki, 305-8571, Japan

    Nobuyuki Ishibashi

  2. Okayama Institute for Quantum Physics, Kyoyama 1-9-1, Kita-ku, Okayama, 700-0015, Japan

    Koichi Murakami

Authors
  1. Nobuyuki Ishibashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Koichi Murakami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koichi Murakami.

Additional information

ArXiv ePrint: 1307.6001

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ishibashi, N., Murakami, K. Multiloop amplitudes of light-cone gauge bosonic string field theory in noncritical dimensions. J. High Energ. Phys. 2013, 53 (2013). https://doi.org/10.1007/JHEP09(2013)053

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP09(2013)053

Keywords

Search

Navigation