Multiloop amplitudes of light-cone gauge superstring field theory: odd spin structure contributions

Abstract

We study the odd spin structure contributions to the multiloop amplitudes of light-cone gauge superstring field theory. We show that they coincide with the amplitudes in the conformal gauge with two of the vertex operators chosen to be in the pictures different from the standard choice, namely (−1, −1) picture in the type II case and −1 picture in the heterotic case. We also show that the contact term divergences can be regularized in the same way as in the amplitudes for the even structures and we get the amplitudes which coincide with those obtained from the first-quantized approach.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    A. Sen, BV master action for heterotic and type II string field theories, JHEP 02 (2016) 087 [arXiv:1508.05387] [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    A. Sen, Gauge invariant 1PI effective action for superstring field theory, JHEP 06 (2015) 022 [arXiv:1411.7478] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  3. [3]

    A. Sen, Gauge invariant 1PI effective superstring field theory: inclusion of the Ramond sector, JHEP 08 (2015) 025 [arXiv:1501.00988] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. [4]

    C. de Lacroix, H. Erbin, S.P. Kashyap, A. Sen and M. Verma, Closed superstring field theory and its applications, Int. J. Mod. Phys. A 32 (2017) 1730021 [arXiv:1703.06410] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  5. [5]

    A. Sen, Background independence of closed superstring field theory, JHEP 02 (2018) 155 [arXiv:1711.08468] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  6. [6]

    B. Zwiebach, Closed string field theory: quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  7. [7]

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

    ADS  MathSciNet  Article  Google Scholar 

  8. [8]

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

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

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

    ADS  Article  Google Scholar 

  10. [10]

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

    ADS  MathSciNet  Article  Google Scholar 

  11. [11]

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

    ADS  MathSciNet  Article  Google Scholar 

  12. [12]

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

    ADS  MathSciNet  Article  Google Scholar 

  13. [13]

    N. Ishibashi and K. Murakami, Multiloop amplitudes of light-cone gauge NSR string field theory in noncritical dimensions, JHEP 01 (2017) 034 [arXiv:1611.06340] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  14. [14]

    N. Ishibashi, Light-cone gauge superstring field theory in linear dilaton background, PTEP 2017 (2017) 033B01 [arXiv:1605.04666] [INSPIRE].

  15. [15]

    Y. Baba, N. Ishibashi and K. Murakami, Light-cone gauge superstring field theory and dimensional regularization, JHEP 10 (2009) 035 [arXiv:0906.3577] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  16. [16]

    N. Ishibashi and K. Murakami, Light-cone gauge NSR strings in noncritical dimensions II — Ramond sector, JHEP 01 (2011) 008 [arXiv:1011.0112] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. [17]

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

    ADS  Article  Google Scholar 

  18. [18]

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

    ADS  MathSciNet  Article  MATH  Google Scholar 

  19. [19]

    E. D’Hoker and D.H. Phong, The geometry of string perturbation theory, Rev. Mod. Phys. 60 (1988) 917 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    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].

    ADS  Article  Google Scholar 

  21. [21]

    S. Arakelov, Intersection theory of divisors on an arithmetic surface, Math. USSR Izv. 8 (1974) 1167.

    MathSciNet  Article  MATH  Google Scholar 

  22. [22]

    E.P. Verlinde and H.L. Verlinde, Multiloop calculations in covariant superstring theory, Phys. Lett. B 192 (1987) 95 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  23. [23]

    A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP 09 (2015) 004 [arXiv:1504.00609] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  24. [24]

    A. Sen, Off-shell amplitudes in superstring theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  25. [25]

    E. Witten, More on superstring perturbation theory: an overview of superstring perturbation theory via super Riemann surfaces, arXiv:1304.2832 [INSPIRE].

  26. [26]

    A. Sen, Supersymmetry restoration in superstring perturbation theory, JHEP 12 (2015) 075 [arXiv:1508.02481] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  27. [27]

    J.J. Atick and A. Sen, Spin field correlators on an arbitrary genus Riemann surface and nonrenormalization theorems in string theories, Phys. Lett. B 186 (1987) 339 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  28. [28]

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

    ADS  MathSciNet  Article  Google Scholar 

  29. [29]

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

    ADS  MathSciNet  Article  Google Scholar 

  30. [30]

    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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  31. [31]

    E.P. Verlinde and H.L. Verlinde, Chiral bosonization, determinants and the string partition function, Nucl. Phys. B 288 (1987) 357 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  32. [32]

    J.D. Fay, Theta functions on Riemann surfaces, Lect. Notes Math. 352, Springer-Verlag, Berlin Heidelberg Germany, (1973).

Download references

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Koichi Murakami.

Additional information

ArXiv ePrint: 1712.09049

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ishibashi, N., Murakami, K. Multiloop amplitudes of light-cone gauge superstring field theory: odd spin structure contributions. J. High Energ. Phys. 2018, 63 (2018). https://doi.org/10.1007/JHEP03(2018)063

Download citation

Keywords

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