Journal of High Energy Physics

, 2016:121 | Cite as

Relating Berkovits and A superstring field theories; large Hilbert space perspective

  • Theodore Erler
Open Access
Regular Article - Theoretical Physics


We lift the dynamical field of the A superstring field theory to the large Hilbert space by introducing a gauge invariance associated with the eta zero mode. We then provide a field redefinition which relates the lifted field to the dynamical field of Berkovits’ superstring field theory in the large Hilbert space. This generalizes the field redefinition in the small Hilbert space described in earlier works, and gives some understanding of the relation between the gauge symmetries of the theories. It also provides a new perspective on the algebraic structure underlying gauge invariance of the Wess-Zumino-Witten-like action.


String Field Theory Superstrings and Heterotic Strings 


Open Access

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  1. [1]
    T. Erler, Y. Okawa and T. Takezaki, A structure from the Berkovits formulation of open superstring field theory, arXiv:1505.01659 [INSPIRE].
  2. [2]
    T. Erler, Relating Berkovits and A superstring field theories; small Hilbert space perspective, JHEP 10 (2015) 157 [arXiv:1505.02069] [INSPIRE].CrossRefADSGoogle Scholar
  3. [3]
    N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
  4. [4]
    N. Berkovits, A new approach to superstring field theory, Fortsch. Phys. 48 (2000) 31 [hep-th/9912121] [INSPIRE].CrossRefADSMathSciNetzbMATHGoogle Scholar
  5. [5]
    T. Erler, S. Konopka and I. Sachs, Resolving Witten‘s superstring field theory, JHEP 04 (2014) 150 [arXiv:1312.2948] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  6. [6]
    N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  7. [7]
    T. Erler, S. Konopka and I. Sachs, NS-NS Sector of Closed Superstring Field Theory, JHEP 08 (2014) 158 [arXiv:1403.0940] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  8. [8]
    K. Goto and H. Matsunaga, On-shell equivalence of two formulations for superstring field theory, arXiv:1506.06657 [INSPIRE].
  9. [9]
    K. Goto and H. Matsunaga, A /L structure and alternative action for WZW-like superstring field theory, arXiv:1512.03379 [INSPIRE].
  10. [10]
    Y. Iimori, T. Noumi, Y. Okawa and S. Torii, From the Berkovits formulation to the Witten formulation in open superstring field theory, JHEP 03 (2014) 044 [arXiv:1312.1677] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  11. [11]
    M. Kroyter, Y. Okawa, M. Schnabl, S. Torii and B. Zwiebach, Open superstring field theory I: gauge fixing, ghost structure and propagator, JHEP 03 (2012) 030 [arXiv:1201.1761] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  12. [12]
    N. Berkovits, Constrained BV Description of String Field Theory, JHEP 03 (2012) 012 [arXiv:1201.1769] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  13. [13]
    S. Torii, Validity of Gauge-Fixing Conditions and the Structure of Propagators in Open Superstring Field Theory, JHEP 04 (2012) 050 [arXiv:1201.1762] [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  14. [14]
    S. Torii, Gauge fixing of open superstring field theory in the Berkovits non-polynomial formulation, Prog. Theor. Phys. Suppl. 188 (2011) 272 [arXiv:1201.1763] [INSPIRE].CrossRefADSzbMATHGoogle Scholar
  15. [15]
    Y. Iimori and S. Torii, Relation between the Reducibility Structures and between the Master Actions in the Witten Formulation and the Berkovits Formulation of Open Superstring Field Theory, JHEP 10 (2015) 127 [arXiv:1507.08757] [INSPIRE].CrossRefADSGoogle Scholar
  16. [16]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].CrossRefADSMathSciNetGoogle Scholar
  17. [17]
    T. Erler, S. Konopka and I. Sachs, Ramond Equations of Motion in Superstring Field Theory, JHEP 11 (2015) 199 [arXiv:1506.05774] [INSPIRE].CrossRefADSGoogle Scholar
  18. [18]
    H. Kunitomo and Y. Okawa, Complete action for open superstring field theory, arXiv:1508.00366 [INSPIRE].
  19. [19]
    A. Sen, Gauge Invariant 1PI Effective Superstring Field Theory: Inclusion of the Ramond Sector, JHEP 08 (2015) 025 [arXiv:1501.00988] [INSPIRE].CrossRefADSGoogle Scholar
  20. [20]
    A. Sen, BV Master Action for Heterotic and Type II String Field Theories, arXiv:1508.05387 [INSPIRE].
  21. [21]
    H. Matsunaga, Comments on complete actions for open superstring field theory, arXiv:1510.06023 [INSPIRE].
  22. [22]
    T. Erler, Y. Okawa and T. Takezaki, Complete Action for Open Superstring Field Theory with Cyclic A Structure, arXiv:1602.02582 [INSPIRE].
  23. [23]
    M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton, U.S.A. (1992), pg. 520.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Arnold Sommerfeld CenterLudwig-Maximilians UniversityMunichGermany

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