Advertisement

Solutions from boundary condition changing operators in open string field theory

  • Michael Kiermaier
  • Yuji Okawa
  • Pablo Soler
Article

Abstract

We construct analytic solutions of open string field theory using boundary condition changing (bcc) operators. We focus on bcc operators with vanishing conformal weight such as those for regular marginal deformations of the background. For any Fock space state ϕ, the component string field \( \left\langle {\phi, \Psi } \right\rangle \) of the solution Ψ exhibits a remarkable factorization property: it is given by the matter three-point function of ϕ with a pair of bcc operators, multiplied by a universal function that only depends on the conformal weight of ϕ. This universal function is given by a simple integral expression that can be computed once and for all. The three-point functions with bcc operators are thus the only needed physical input of the particular open string background described by the solution. We illustrate our solution with the example of the rolling tachyon profile, for which we prove convergence analytically. The form of our solution, which involves bcc operators instead of explicit insertions of the marginal operator, can be a natural starting point for the construction of analytic solutions for arbitrary backgrounds.

Keywords

Tachyon Condensation Bosonic Strings String Field Theory Boundary Quantum Field Theory 

References

  1. [1]
    E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [SPIRES].MathSciNetADSCrossRefGoogle 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] [SPIRES].MathSciNetMATHGoogle 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] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    E. Fuchs and M. Kroyter, On the validity of the solution of string field theory, JHEP 05 (2006) 006 [hep-th/0603195] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    E. Fuchs and M. Kroyter, Schnabl’s \( {\mathcal{L}_0} \) operator in the continuous basis, JHEP 10 (2006) 067 [hep-th/0605254] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    L. Rastelli and B. Zwiebach, Solving open string field theory with special projectors, JHEP 01 (2008) 020 [hep-th/0606131] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    I. Ellwood and M. Schnabl, Proof of vanishing cohomology at the tachyon vacuum, JHEP 02 (2007) 096 [hep-th/0606142] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    H. Fuji, S. Nakayama and H. Suzuki, Open string amplitudes in various gauges, JHEP 01 (2007) 011 [hep-th/0609047] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    E. Fuchs and M. Kroyter, Universal regularization for string field theory, JHEP 02 (2007) 038 [hep-th/0610298] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for tachyon condensation with general projectors, hep-th/0611110 [SPIRES].
  11. [11]
    T. Erler, Split string formalism and the closed string vacuum, JHEP 05 (2007) 083 [hep-th/0611200] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    T. Erler, Split string formalism and the closed string vacuum. II, JHEP 05 (2007) 084 [hep-th/0612050] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    M. Schnabl, Comments on marginal deformations in open string field theory, Phys. Lett. B 654 (2007) 194 [hep-th/0701248] [SPIRES].MathSciNetADSGoogle Scholar
  14. [14]
    M. Kiermaier, Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for marginal deformations in open string field theory, JHEP 01 (2008) 028 [hep-th/0701249] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    T. Erler, Marginal solutions for the superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    E. Fuchs, M. Kroyter and R. Potting, Marginal deformations in string field theory, JHEP 09 (2007) 101 [arXiv:0704.2222] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    Y. Okawa, Real analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 082 [arXiv:0704.3612] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    I. Ellwood, Rolling to the tachyon vacuum in string field theory, JHEP 12 (2007) 028 [arXiv:0705.0013] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    I. Kishimoto and Y. Michishita, Comments on solutions for nonsingular currents in open string field theories, Prog. Theor. Phys. 118 (2007) 347 [arXiv:0706.0409] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  21. [21]
    E. Fuchs and M. Kroyter, Marginal deformation for the photon in superstring field theory, JHEP 11 (2007) 005 [arXiv:0706.0717] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    M. Kiermaier and Y. Okawa, Exact marginality in open string field theory: a general framework, JHEP 11 (2009) 041 [arXiv:0707.4472] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    T. Erler, Tachyon vacuum in cubic superstring field theory, JHEP 01 (2008) 013 [arXiv:0707.4591] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    L. Rastelli and B. Zwiebach, The off-shell Veneziano amplitude in Schnabl gauge, JHEP 01 (2008) 018 [arXiv:0708.2591] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    M. Kiermaier and Y. Okawa, General marginal deformations in open superstring field theory, JHEP 11 (2009) 042 [arXiv:0708.3394] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    O.-K. Kwon, B.-H. Lee, C. Park and S.-J. Sin, Fluctuations around the tachyon vacuum in open string field theory, JHEP 12 (2007) 038 [arXiv:0709.2888] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    T. Takahashi, Level truncation analysis of exact solutions in open string field theory, JHEP 01 (2008) 001 [arXiv:0710.5358] [SPIRES].ADSCrossRefGoogle Scholar
  28. [28]
    M. Kiermaier, A. Sen and B. Zwiebach, Linear b-gauges for open string fields, JHEP 03 (2008) 050 [arXiv:0712.0627] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    O.-K. Kwon, Marginally deformed rolling tachyon around the tachyon vacuum in open string field theory, Nucl. Phys. B 804 (2008) 1 [arXiv:0801.0573] [SPIRES].ADSCrossRefGoogle Scholar
  30. [30]
    S. Hellerman and M. Schnabl, Light-like tachyon condensation in open string field theory, arXiv:0803.1184 [SPIRES].
  31. [31]
    I. Ellwood, The closed string tadpole in open string field theory, JHEP 08 (2008) 063 [arXiv:0804.1131] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  32. [32]
    T. Kawano, I. Kishimoto and T. Takahashi, Gauge invariant overlaps for classical solutions in open string field theory, Nucl. Phys. B 803 (2008) 135 [arXiv:0804.1541] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    I.Y. Aref’eva, R.V. Gorbachev and P.B. Medvedev, Tachyon solution in cubic Neveu-Schwarz string field theory, Theor. Math. Phys. 158 (2009) 320 [arXiv:0804.2017] [SPIRES].MathSciNetCrossRefGoogle Scholar
  34. [34]
    A. Ishida, C. Kim, Y. Kim, O.-K. Kwon and D.D. Tolla, Tachyon vacuum solution in open string field theory with constant B field, J. Phys. A 42 (2009) 395402 [arXiv:0804.4380] [SPIRES].MathSciNetGoogle Scholar
  35. [35]
    T. Kawano, I. Kishimoto and T. Takahashi, Schnabl’s solution and boundary states in open string field theory, Phys. Lett. B 669 (2008) 357 [arXiv:0804.4414] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    M. Kiermaier and B. Zwiebach, One-loop riemann surfaces in Schnabl gauge, JHEP 07 (2008) 063 [arXiv:0805.3701] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  37. [37]
    E. Fuchs and M. Kroyter, Analytical solutions of open string field theory, arXiv:0807.4722 [SPIRES].
  38. [38]
    M. Asano and M. Kato, General linear gauges and amplitudes in open string field theory, Nucl. Phys. B 807 (2009) 348 [arXiv:0807.5010] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  39. [39]
    I. Kishimoto, Comments on gauge invariant overlaps for marginal solutions in open string field theory, Prog. Theor. Phys. 120 (2008) 875 [arXiv:0808.0355] [SPIRES].ADSMATHCrossRefGoogle Scholar
  40. [40]
    M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [SPIRES].
  41. [41]
    N. Barnaby, D.J. Mulryne, N.J. Nunes and P. Robinson, Dynamics and stability of light-like tachyon condensation, JHEP 03 (2009) 018 [arXiv:0811.0608] [SPIRES].ADSCrossRefGoogle Scholar
  42. [42]
    I.Y. Aref’eva et al., Pure gauge configurations and tachyon solutions to string field theories equations of motion, JHEP 05 (2009) 050 [arXiv:0901.4533] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    I. Kishimoto and T. Takahashi, Numerical evaluation of gauge invariants for a-gauge solutions in open string field theory, Prog. Theor. Phys. 121 (2009) 695 [arXiv:0902.0445] [SPIRES].ADSMATHCrossRefGoogle Scholar
  44. [44]
    I. Ellwood, Singular gauge transformations in string field theory, JHEP 05 (2009) 037 [arXiv:0903.0390] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  45. [45]
    I.Y. Aref’eva, R.V. Gorbachev and P.B. Medvedev, Pure gauge configurations and solutions to fermionic superstring field theories equations of motion, J. Phys. A 42 (2009) 304001 [arXiv:0903.1273] [SPIRES].MathSciNetGoogle Scholar
  46. [46]
    E.A. Arroyo, Cubic interaction term for Schnabl’s solution using Pade approximants, J. Phys. A 42 (2009) 375402 [arXiv:0905.2014] [SPIRES].MathSciNetGoogle Scholar
  47. [47]
    M. Kroyter, Comments on superstring field theory and its vacuum solution, JHEP 08 (2009) 048 [arXiv:0905.3501] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    T. Erler and M. Schnabl, A simple analytic solution for tachyon condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    E. Aldo Arroyo, The tachyon potential in the sliver frame, JHEP 10 (2009) 056 [arXiv:0907.4939] [SPIRES].ADSCrossRefGoogle Scholar
  50. [50]
    F. Beaujean and N. Moeller, Delays in open string field theory, arXiv:0912.1232 [SPIRES].
  51. [51]
    E.A. Arroyo, Generating Erler-Schnabl-type solution for tachyon vacuum in cubic superstring field theory, J. Phys. A 43 (2010) 445403 [arXiv:1004.3030] [SPIRES].MathSciNetADSGoogle Scholar
  52. [52]
    S. Zeze, Tachyon potential in KBc subalgebra, Prog. Theor. Phys. 124 (2011) 567 [arXiv:1004.4351] [SPIRES].ADSCrossRefGoogle Scholar
  53. [53]
    M. Schnabl, Algebraic solutions in open string field theory — A lightning review, arXiv:1004.4858 [SPIRES].
  54. [54]
    I.Y. Arefeva and R.V. Gorbachev, On gauge equivalence of tachyon solutions in cubic Neveu-Schwarz string field theory, Theor. Math. Phys. 165 (2010) 1512 [arXiv:1004.5064] [SPIRES].CrossRefGoogle Scholar
  55. [55]
    S. Zeze, Regularization of identity based solution in string field theory, JHEP 10 (2010) 070 [arXiv:1008.1104] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  56. [56]
    E.A. Arroyo, Comments on regularization of identity based solutions in string field theory, JHEP 11 (2010) 135 [arXiv:1009.0198] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  57. [57]
    T. Erler, Exotic universal solutions in cubic superstring field theory, arXiv:1009.1865 [SPIRES].
  58. [58]
    L. Bonora, C. Maccaferri and D.D. Tolla, Relevant deformations in open string field theory: a simple solution for lumps, arXiv:1009.4158 [SPIRES].
  59. [59]
    A. Hashimoto and N. Itzhaki, Observables of string field theory, JHEP 01 (2002) 028 [hep-th/0111092] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  60. [60]
    D. Gaiotto, L. Rastelli, A. Sen and B. Zwiebach, Ghost structure and closed strings in vacuum string field theory, Adv. Theor. Math. Phys. 6 (2003) 403 [hep-th/0111129] [SPIRES].MathSciNetGoogle Scholar
  61. [61]
    L. Rastelli and B. Zwiebach, Tachyon potentials, star products and universality, JHEP 09 (2001) 038 [hep-th/0006240] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  62. [62]
    A. Bagchi and A. Sen, Tachyon condensation on separated brane-antibrane system, JHEP 05 (2008) 010 [arXiv:0801.3498] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  63. [63]
    M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories I: foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  64. [64]
    A. Sen, Rolling tachyon, JHEP 04 (2002) 048 [hep-th/0203211] [SPIRES].ADSCrossRefGoogle Scholar
  65. [65]
    A. Sen, Tachyon matter, JHEP 07 (2002) 065 [hep-th/0203265] [SPIRES].ADSCrossRefGoogle Scholar
  66. [66]
    A. Sen, Time evolution in open string theory, JHEP 10 (2002) 003 [hep-th/0207105] [SPIRES].ADSCrossRefGoogle Scholar
  67. [67]
    N. Moeller and B. Zwiebach, Dynamics with infinitely many time derivatives and rolling tachyons, JHEP 10 (2002) 034 [hep-th/0207107] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  68. [68]
    F. Larsen, A. Naqvi and S. Terashima, Rolling tachyons and decaying branes, JHEP 02 (2003) 039 [hep-th/0212248] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  69. [69]
    N.D. Lambert, H. Liu and J.M. Maldacena, Closed strings from decaying D-branes, JHEP 03 (2007) 014 [hep-th/0303139] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  70. [70]
    M. Fujita and H. Hata, Time dependent solution in cubic string field theory, JHEP 05 (2003) 043 [hep-th/0304163] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  71. [71]
    D. Gaiotto, N. Itzhaki and L. Rastelli, Closed strings as imaginary D-branes, Nucl. Phys. B 688 (2004) 70 [hep-th/0304192] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  72. [72]
    T. Erler, Level truncation and rolling the tachyon in the lightcone basis for open string field theory, hep-th/0409179 [SPIRES].
  73. [73]
    A. Sen, Tachyon dynamics in open string theory, Int. J. Mod. Phys. A 20 (2005) 5513 [hep-th/0410103] [SPIRES].ADSGoogle Scholar
  74. [74]
    E. Coletti, I. Sigalov and W. Taylor, Taming the tachyon in cubic string field theory, JHEP 08 (2005) 104 [hep-th/0505031] [SPIRES].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.Princeton UniversityPrincetonU.S.A.
  2. 2.Institute of PhysicsUniversity of TokyoTokyoJapan
  3. 3.Instituto de Física Teórica UAM/CSICUniversidad Autónoma de Madrid C-XVIMadridSpain

Personalised recommendations