Open superstring field theory based on the supermoduli space

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Regular Article - Theoretical Physics
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Abstract

We present a new approach to formulating open superstring field theory based on the covering of the supermoduli space of super-Riemann surfaces and explicitly construct a gauge-invariant action in the Neveu-Schwarz sector up to quartic interactions. The cubic interaction takes a form of an integral over an odd modulus of disks with three punctures and the associated ghost is inserted. The quartic interaction takes a form of an integral over one even modulus and two odd moduli, and it can be interpreted as the integral over the region of the supermoduli space of disks with four punctures which is not covered by Feynman diagrams with two cubic vertices and one propagator. As our approach is based on the covering of the supermoduli space, the resulting theory naturally realizes an A structure, and the two-string product and the three-string product used in defining the cubic and quartic interactions are constructed to satisfy the A relations to this order.

Keywords

String Field Theory Superstrings and Heterotic Strings 

Notes

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References

  1. [1]
    E. Witten, Noncommutative Geometry and String Field Theory, Nucl. Phys. B 268 (1986) 253 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys. 10 (2006) 433 [hep-th/0511286] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Y. Okawa, Comments on Schnabl’s analytic solution for tachyon condensation in Witten’s open string field theory, JHEP 04 (2006) 055 [hep-th/0603159] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    J.D. Stasheff, Homotopy associativity of H-spaces. I, Trans. Am. Math. Soc. 108 (1963) 275.Google Scholar
  5. [5]
    J.D. Stasheff, Homotopy associativity of H-spaces. II, Trans. Am. Math. Soc. 108 (1963) 293.Google Scholar
  6. [6]
    E. Getzler and J.D.S. Jones, A -algebras and the cyclic bar complex, Illinois J. Math 34 (1990) 256.MathSciNetMATHGoogle Scholar
  7. [7]
    M. Markl, A cohomology theory for A(m)-algebras and applications, J. Pure Appl. Algebra 83 (1992) 141.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    M. Penkava and A.S. Schwarz, A algebras and the cohomology of moduli spaces, hep-th/9408064 [INSPIRE].
  9. [9]
    M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories. 1: Foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [INSPIRE].
  10. [10]
    I.A. Batalin and G.A. Vilkovisky, Gauge Algebra and Quantization, Phys. Lett. B 102 (1981) 27 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    I.A. Batalin and G.A. Vilkovisky, Quantization of Gauge Theories with Linearly Dependent Generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].
  12. [12]
    B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    T. Lada and J. Stasheff, Introduction to SH Lie algebras for physicists, Int. J. Theor. Phys. 32 (1993) 1087 [hep-th/9209099] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  14. [14]
    M. Schlessinger and J. Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985) 313.MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    N. Berkovits, SuperPoincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [Erratum ibid. B 459 (1996) 439] [hep-th/9503099] [INSPIRE].
  16. [16]
    D. Friedan, E.J. Martinec and S.H. Shenker, Conformal Invariance, Supersymmetry and String Theory, Nucl. Phys. B 271 (1986) 93 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  18. [18]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    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].ADSCrossRefMATHGoogle Scholar
  20. [20]
    N. Berkovits, Constrained BV Description of String Field Theory, JHEP 03 (2012) 012 [arXiv:1201.1769] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    N. Berkovits, M. Kroyter, Y. Okawa, M. Schnabl, S. Torii and B. Zwiebach, Open superstring field theory II: approaches to the BV master action, to appear.Google Scholar
  22. [22]
    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].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    A. Sen, Off-shell Amplitudes in Superstring Theory, Fortsch. Phys. 63 (2015) 149 [arXiv:1408.0571] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    A. Sen and E. Witten, Filling the gaps with PCO’s, JHEP 09 (2015) 004 [arXiv:1504.00609] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  25. [25]
    T. Erler, S. Konopka and I. Sachs, Resolving Witten‘s superstring field theory, JHEP 04 (2014) 150 [arXiv:1312.2948] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [26]
    T. Erler, S. Konopka and I. Sachs, NS-NS Sector of Closed Superstring Field Theory, JHEP 08 (2014) 158 [arXiv:1403.0940] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    T. Erler, S. Konopka and I. Sachs, Ramond Equations of Motion in Superstring Field Theory, JHEP 11 (2015) 199 [arXiv:1506.05774] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    T. Erler, Y. Okawa and T. Takezaki, A structure from the Berkovits formulation of open superstring field theory, arXiv:1505.01659 [INSPIRE].
  29. [29]
    T. Erler, Relating Berkovits and A superstring field theories; small Hilbert space perspective, JHEP 10 (2015) 157 [arXiv:1505.02069] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    T. Erler, Relating Berkovits and A superstring field theories; large Hilbert space perspective, JHEP 02 (2016) 121 [arXiv:1510.00364] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  31. [31]
    H. Kunitomo and Y. Okawa, Complete action for open superstring field theory, PTEP 2016 (2016) 023B01 [arXiv:1508.00366] [INSPIRE].
  32. [32]
    T. Erler, Y. Okawa and T. Takezaki, Complete Action for Open Superstring Field Theory with Cyclic A Structure, JHEP 08 (2016) 012 [arXiv:1602.02582] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    S. Konopka and I. Sachs, Open Superstring Field Theory on the Restricted Hilbert Space, JHEP 04 (2016) 164 [arXiv:1602.02583] [INSPIRE].ADSMathSciNetGoogle Scholar
  34. [34]
    A. Sen, BV Master Action for Heterotic and Type II String Field Theories, JHEP 02 (2016) 087 [arXiv:1508.05387] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    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].MathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    A. Sen, Gauge Invariant 1PI Effective Superstring Field Theory: Inclusion of the Ramond Sector, JHEP 08 (2015) 025 [arXiv:1501.00988] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  37. [37]
    H. Kunitomo, Y. Okawa, H. Sukeno and T. Takezaki, Fermion scattering amplitudes from gauge-invariant actions for open superstring field theory, arXiv:1612.00777 [INSPIRE].
  38. [38]
    K. Goto and H. Kunitomo, Construction of action for heterotic string field theory including the Ramond sector, JHEP 12 (2016) 157 [arXiv:1606.07194] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    T. Erler, Supersymmetry in Open Superstring Field Theory, JHEP 05 (2017) 113 [arXiv:1610.03251] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    H. Kunitomo, Space-time supersymmetry in WZW-like open superstring field theory, PTEP 2017 (2017) 043B04 [arXiv:1612.08508] [INSPIRE].
  41. [41]
    E. Witten, Superstring Perturbation Theory Revisited, arXiv:1209.5461 [INSPIRE].
  42. [42]
    E. Witten, Notes On Super Riemann Surfaces And Their Moduli, arXiv:1209.2459 [INSPIRE].
  43. [43]
    O. Lechtenfeld, Superconformal ghost correlations on Riemann surfaces, Phys. Lett. B 232 (1989) 193 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    A. Morozov, Straightforward proof of Lechtenfeld’s formula for β, γ-correlator, Phys. Lett. B 234 (1990) 15 [INSPIRE].ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Department of PhysicsThe University of TokyoTokyoJapan
  2. 2.School of Natural SciencesInstitute for Advanced StudyPrincetonU.S.A.
  3. 3.Institute of PhysicsThe University of TokyoTokyoJapan

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