Advertisement

Worldsheet theory of light-cone gauge noncritical strings on higher genus Riemann surfaces

  • Nobuyuki Ishibashi
  • Koichi Murakami
Open Access
Regular Article - Theoretical Physics

Abstract

It is possible to formulate light-cone gauge string field theory in noncritical dimensions. Such a theory corresponds to conformal gauge worldsheet theory with nonstandard longitudinal part. We study the longitudinal part of the worldsheet theory on higher genus Riemann surfaces. The results in this paper shall be used to study the dimensional regularization of light-cone gauge string field theory.

Keywords

String Field Theory BRST Quantization Conformal Field Models in String Theory Superstrings and Heterotic Strings 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    Y. Baba, N. Ishibashi and K. Murakami, Light-Cone Gauge String Field Theory in Noncritical Dimensions, JHEP 12 (2009) 010 [arXiv:0909.4675] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    Y. Baba, N. Ishibashi and K. Murakami, Light-cone Gauge NSR Strings in Noncritical Dimensions, JHEP 01 (2010) 119 [arXiv:0911.3704] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Y. Baba, N. Ishibashi and K. Murakami, Light-Cone Gauge Superstring Field Theory and Dimensional Regularization, JHEP 10 (2009) 035 [arXiv:0906.3577] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    N. Ishibashi and K. Murakami, Light-cone Gauge NSR Strings in Noncritical Dimensions II — Ramond Sector, JHEP 01 (2011) 008 [arXiv:1011.0112] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    J. Greensite and F.R. Klinkhamer, New Interactions for Superstrings, Nucl. Phys. B 281 (1987) 269 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    J. Greensite and F.R. Klinkhamer, Superstring Amplitudes and Contact Interactions, Nucl. Phys. B 304 (1988) 108 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Greensite and F.R. Klinkhamer, Contact Interactions in Closed Superstring Field Theory, Nucl. Phys. B 291 (1987) 557 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    M.B. Green and N. Seiberg, Contact Interactions in Superstring Theory, Nucl. Phys. B 299 (1988) 559 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    C. Wendt, Scattering Amplitudes and Contact Interactions in Witten’s Superstring Field Theory, Nucl. Phys. B 314 (1989) 209 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    N. Ishibashi and K. Murakami, Multiloop Amplitudes of Light-cone Gauge Bosonic String Field Theory in Noncritical Dimensions, JHEP 09 (2013) 053 [arXiv:1307.6001] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    E. D’Hoker and D.H. Phong, The Geometry of String Perturbation Theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    S. Mandelstam, The interacting string picture and functional integration, in proceedings of Workshop on unified string theories, Santa Barbara, CA, U.S.A. 29 July–16 August 1985.Google Scholar
  15. [15]
    L. Álvarez-Gaumé, J.B. Bost, G.W. Moore, P.C. Nelson and C. Vafa, Bosonization on Higher Genus Riemann Surfaces, Commun. Math. Phys. 112 (1987) 503 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    E.P. Verlinde and H.L. Verlinde, Chiral Bosonization, Determinants and the String Partition Function, Nucl. Phys. B 288 (1987) 357 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    M.J. Dugan and H. Sonoda, Functional determinants on Riemann surfaces, Nucl. Phys. B 289 (1987) 227 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    H. Sonoda, Functional Determinants on Punctured Riemann Surfaces and Their Application to String Theory, Nucl. Phys. B 294 (1987) 157 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    R. Wentworth, The asymptotics of the arakelov-green’s function and faltings’ delta invariant, Commun. Math. Phys. 137 (1991) 427.ADSMathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    R.A. Wentworth, Precise constants in bosonization formulas on Riemann surfaces. I, Commun. Math. Phys. 282 (2008) 339.ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    G. Faltings, Calculus on arithmetic surfaces, Ann. Math. 119 (1984) 387.MathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    N. Berkovits, Calculation of Scattering Amplitudes for the Neveu-Schwarz Model Using Supersheet Functional Integration, Nucl. Phys. B 276 (1986) 650 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    N. Berkovits, Supersheet Functional Integration and the Interacting Neveu-Schwarz String, Nucl. Phys. B 304 (1988) 537 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    K. Aoki, E. D’Hoker and D.H. Phong, Unitarity of Closed Superstring Perturbation Theory, Nucl. Phys. B 342 (1990) 149 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  25. [25]
    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].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    N. Berkovits, The Heterotic Green-Schwarz superstring on an N = (2, 0) superworldsheet, Nucl. Phys. B 379 (1992) 96 [hep-th/9201004] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  27. [27]
    N. Berkovits, Calculation of Green-Schwarz superstring amplitudes using the N = 2 twistor string formalism, Nucl. Phys. B 395 (1993) 77 [hep-th/9208035] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    N.J. Berkovits and J.M. Maldacena, N = 2 superconformal description of superstring in Ramond-Ramond plane wave backgrounds, JHEP 10 (2002) 059 [hep-th/0208092] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  29. [29]
    M.B. Green and J.H. Schwarz, Superstring Interactions, Nucl. Phys. B 218 (1983) 43 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    M.B. Green, J.H. Schwarz and L. Brink, Superfield Theory of Type II Superstrings, Nucl. Phys. B 219 (1983) 437 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    E. D’Hoker and D.H. Phong, Functional determinants on Mandelstam diagrams, Commun. Math. Phys. 124 (1989) 629 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    S. Mandelstam, The n loop string amplitude: Explicit formulas, finiteness and absence of ambiguities, Phys. Lett. B 277 (1992) 82 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Graduate School of Pure and Applied SciencesUniversity of TsukubaTsukubaJapan
  2. 2.National Institute of TechnologyKushiro CollegeKushiroJapan

Personalised recommendations