String field theory solution for any open string background

Open Access
Article

Abstract

We present an exact solution of open bosonic string field theory which can be used to describe any time-independent open string background. The solution generalizes an earlier construction of Kiermaier, Okawa, and Soler, and assumes the existence of boundary condition changing operators with nonsingular OPEs and vanishing conformal dimension. Our main observation is that boundary condition changing operators of this kind can describe nearly any open string background provided the background shift is accompanied by a timelike Wilson line of sufficient strength. As an application we analyze the tachyon lump describing the formation of a D(p−1)-brane in the string field theory of a Dp-brane, for generic compactification radius. This not only provides a proof of Sen’s second conjecture, but also gives explicit examples of higher energy solutions, confirming analytically that string field theory can “reverse” the direction of the worldsheet RG flow. We also find multiple D-brane solutions, demonstrating that string field theory can add Chan-Paton factors and change the rank of the gauge group. Finally, we show how the solution provides a remarkably simple and nonperturbative proof of the background independence of open bosonic string field theory.

Keywords

Tachyon Condensation String Field Theory Conformal Field Models in String Theory Bosonic Strings 

References

  1. [1]
    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
  2. [2]
    I. Ellwood and M. Schnabl, Proof of vanishing cohomology at the tachyon vacuum, JHEP 02 (2007) 096 [hep-th/0606142] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    T. Erler and M. Schnabl, A simple analytic solution for tachyon condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  4. [4]
    T. Erler, Analytic solution for tachyon condensation in Berkovitsopen superstring field theory, JHEP 11 (2013) 007 [arXiv:1308.4400] [INSPIRE].ADSCrossRefGoogle Scholar
  5. [5]
    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] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    M. Schnabl, Comments on marginal deformations in open string field theory, Phys. Lett. B 654 (2007) 194 [hep-th/0701248] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    E. Fuchs, M. Kroyter and R. Potting, Marginal deformations in string field theory, JHEP 09 (2007) 101 [arXiv:0704.2222] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    M. Kiermaier and Y. Okawa, Exact marginality in open string field theory: a general framework, JHEP 11 (2009) 041 [arXiv:0707.4472] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  9. [9]
    T. Erler, Marginal solutions for the superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    Y. Okawa, Real analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 082 [arXiv:0704.3612] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    E. Fuchs and M. Kroyter, Marginal deformation for the photon in superstring field theory, JHEP 11 (2007) 005 [arXiv:0706.0717] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [13]
    M. Kiermaier and Y. Okawa, General marginal deformations in open superstring field theory, JHEP 11 (2009) 042 [arXiv:0708.3394] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  14. [14]
    M. Kiermaier, Y. Okawa and P. Soler, Solutions from boundary condition changing operators in open string field theory, JHEP 03 (2011) 122 [arXiv:1009.6185] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    T. Takahashi and S. Tanimoto, Marginal and scalar solutions in cubic open string field theory, JHEP 03 (2002) 033 [hep-th/0202133] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Inatomi, I. Kishimoto and T. Takahashi, Tachyon vacuum of bosonic open string field theory in marginally deformed backgrounds, PTEP 2013 (2013) 023B02 [arXiv:1209.4712] [INSPIRE].Google Scholar
  17. [17]
    I. Kishimoto and T. Takahashi, Gauge invariant overlaps for identity-based marginal solutions, arXiv:1307.1203 [INSPIRE].
  18. [18]
    S. Inatomi, I. Kishimoto and T. Takahashi, On nontrivial solutions around a marginal solution in cubic superstring field theory, JHEP 12 (2012) 071 [arXiv:1209.6107] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    I. Kishimoto and T. Takahashi, Comments on observables for identity-based marginal solutions in Berkovitssuperstring field theory, JHEP 07 (2014) 031 [arXiv:1404.4427] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    C. Maccaferri, A simple solution for marginal deformations in open string field theory, JHEP 05 (2014) 004 [arXiv:1402.3546] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  21. [21]
    A. Sen and B. Zwiebach, Large marginal deformations in string field theory, JHEP 10 (2000) 009 [hep-th/0007153] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    A. Sen, Energy momentum tensor and marginal deformations in open string field theory, JHEP 08 (2004) 034 [hep-th/0403200] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  23. [23]
    J.L. Karczmarek and M. Longton, SFT on separated D-branes and D-brane translation, JHEP 08 (2012) 057 [arXiv:1203.3805] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  24. [24]
    M. Kudrna, T. Masuda, Y. Okawa, M. Schnabl and K. Yoshida, Gauge-invariant observables and marginal deformations in open string field theory, JHEP 01 (2013) 103 [arXiv:1207.3335] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    I. Ellwood, Singular gauge transformations in string field theory, JHEP 05 (2009) 037 [arXiv:0903.0390] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    L. Bonora, C. Maccaferri and D.D. Tolla, Relevant deformations in open string field theory: a simple solution for lumps, JHEP 11 (2011) 107 [arXiv:1009.4158] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    L. Bonora, S. Giaccari and D.D. Tolla, The energy of the analytic lump solution in SFT, JHEP 08 (2011) 158 [Erratum ibid. 1204 (2012) 001] [arXiv:1105.5926] [INSPIRE].
  28. [28]
    T. Erler and C. Maccaferri, Comments on lumps from RG flows, JHEP 11 (2011) 092 [arXiv:1105.6057] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  29. [29]
    T. Erler and C. Maccaferri, Connecting Solutions in Open String Field Theory with Singular Gauge Transformations, JHEP 04 (2012) 107 [arXiv:1201.5119] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    L. Bonora and S. Giaccari, Generalized states in SFT, Eur. Phys. J. C 73 (2013) 2644 [arXiv:1304.2159] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  31. [31]
    T. Noumi and Y. Okawa, Solutions from boundary condition changing operators in open superstring field theory, JHEP 12 (2011) 034 [arXiv:1108.5317] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    Y. Okawa, Comments on Schnabls analytic solution for tachyon condensation in Wittens open string field theory, JHEP 04 (2006) 055 [hep-th/0603159] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    T. Erler, Split string formalism and the closed string vacuum, JHEP 05 (2007) 083 [hep-th/0611200] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  34. [34]
    Y. Okawa, Analytic methods in open string field theory, Prog. Theor. Phys. 128 (2012) 1001 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  35. [35]
    A. Sen, Rolling tachyon, JHEP 04 (2002) 048 [hep-th/0203211] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  36. [36]
    I. Ellwood, Rolling to the tachyon vacuum in string field theory, JHEP 12 (2007) 028 [arXiv:0705.0013] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    S. Hellerman and M. Schnabl, Light-like tachyon condensation in open string field theory, JHEP 04 (2013) 005 [arXiv:0803.1184] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [38]
    D. Ghoshal and P. Patcharamaneepakorn, Travelling front of a decaying brane in string field theory, JHEP 03 (2014) 015 [arXiv:1307.4890] [INSPIRE].ADSCrossRefGoogle Scholar
  39. [39]
    M. Schnabl, Wedge states in string field theory, JHEP 01 (2003) 004 [hep-th/0201095] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  40. [40]
    L. Rastelli and B. Zwiebach, Tachyon potentials, star products and universality, JHEP 09 (2001) 038 [hep-th/0006240] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    L. Rastelli, A. Sen and B. Zwiebach, Boundary CFT construction of D-branes in vacuum string field theory, JHEP 11 (2001) 045 [hep-th/0105168] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  42. [42]
    Y. Okawa, L. Rastelli and B. Zwiebach, Analytic solutions for tachyon condensation with general projectors, hep-th/0611110 [INSPIRE].
  43. [43]
    T. Erler, Tachyon vacuum in cubic superstring field theory, JHEP 01 (2008) 013 [arXiv:0707.4591] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  44. [44]
    E. Witten, On background independent open string field theory, Phys. Rev. D 46 (1992) 5467 [hep-th/9208027] [INSPIRE].ADSMathSciNetGoogle Scholar
  45. [45]
    D. Kutasov, M. Mariño and G.W. Moore, Some exact results on tachyon condensation in string field theory, JHEP 10 (2000) 045 [hep-th/0009148] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories. 1: Foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  47. [47]
    L. Rastelli and B. Zwiebach, Solving open string fieldl theory with special projectors, JHEP 01 (2008) 020 [hep-th/0606131] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    J.A. Shapiro and C.B. Thorn, Closed string-open string transitions and Wittens string field theory, Phys. Lett. B 194 (1987) 43 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    J.A. Shapiro and C.B. Thorn, BRST invariant transitions between closed and open strings, Phys. Rev. D 36 (1987) 432 [INSPIRE].ADSMathSciNetGoogle Scholar
  50. [50]
    A. Hashimoto and N. Itzhaki, Observables of string field theory, JHEP 01 (2002) 028 [hep-th/0111092] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    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] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    I. Ellwood, The closed string tadpole in open string field theory, JHEP 08 (2008) 063 [arXiv:0804.1131] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [INSPIRE].
  54. [54]
    M. Kudrna, C. Maccaferri and M. Schnabl, Boundary state from Ellwood invariants, JHEP 07 (2013) 033 [arXiv:1207.4785] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  55. [55]
    C. Imbimbo, The spectrum of open string field theory at the stable tachyonic vacuum, Nucl. Phys. B 770 (2007) 155 [hep-th/0611343] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  56. [56]
    I. Kishimoto and T. Takahashi, Open string field theory around universal solutions, Prog. Theor. Phys. 108 (2002) 591 [hep-th/0205275] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    S. Inatomi, I. Kishimoto and T. Takahashi, Homotopy operators and identity-based solutions in cubic superstring field theory, JHEP 10 (2011) 114 [arXiv:1109.2406] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  58. [58]
    E. Fuchs and M. Kroyter, On the validity of the solution of string field theory, JHEP 05 (2006) 006 [hep-th/0603195] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    Y. Okawa, Some exact computations on the twisted butterfly state in string field theory, JHEP 01 (2004) 066 [hep-th/0310264] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  60. [60]
    T. Baba and N. Ishibashi, Energy from the gauge invariant observables, JHEP 04 (2013) 050 [arXiv:1208.6206] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  61. [61]
    A. Recknagel and V. Schomerus, Boundary deformation theory and moduli spaces of D-branes, Nucl. Phys. B 545 (1999) 233 [hep-th/9811237] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  62. [62]
    A. Sen, On the background independence of string field theory, Nucl. Phys. B 345 (1990) 551 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    A. Sen, On the background independence of string field theory. 2. Analysis of on-shell S matrix elements, Nucl. Phys. B 347 (1990) 270 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  64. [64]
    A. Sen, On the background independence of string field theory. 3. Explicit field redefinitions, Nucl. Phys. B 391 (1993) 550 [hep-th/9201041] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  65. [65]
    A. Sen and B. Zwiebach, A proof of local background independence of classical closed string field theory, Nucl. Phys. B 414 (1994) 649 [hep-th/9307088] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  66. [66]
    T. Erler, The identity string field and the Sliver frame level expansion, JHEP 11 (2012) 150 [arXiv:1208.6287] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    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] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  68. [68]
    T. Erler, Split string formalism and the closed string vacuum, II, JHEP 05 (2007) 084 [hep-th/0612050] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    T. Erler, Exotic universal solutions in cubic superstring field theory, JHEP 04 (2011) 107 [arXiv:1009.1865] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  70. [70]
    T. Erler and C. Maccaferri, The phantom term in open string field theory, JHEP 06 (2012) 084 [arXiv:1201.5122] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  71. [71]
    M. Murata and M. Schnabl, Multibrane solutions in open string field theory, JHEP 07 (2012) 063 [arXiv:1112.0591] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  72. [72]
    N. Moeller, A. Sen and B. Zwiebach, D-branes as tachyon lumps in string field theory, JHEP 08 (2000) 039 [hep-th/0005036] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  73. [73]
    N. Moeller, Codimension two lump solutions in string field theory and tachyonic theories, hep-th/0008101 [INSPIRE].
  74. [74]
    M. Beccaria, D0-brane tension in string field theory, JHEP 09 (2005) 021 [hep-th/0508090] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  75. [75]
    L.J. Dixon, D. Friedan, E.J. Martinec and S.H. Shenker, The conformal field theory of orbifolds, Nucl. Phys. B 282 (1987) 13 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  76. [76]
    E. Gava, K.S. Narain and M.H. Sarmadi, On the bound states of p-branes and (p +2)-branes, Nucl. Phys. B 504 (1997) 214 [hep-th/9704006] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  77. [77]
    J. Fröhlich, O. Grandjean, A. Recknagel and V. Schomerus, Fundamental strings in Dp-Dq brane systems, Nucl. Phys. B 583 (2000) 381 [hep-th/9912079] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  78. [78]
    P. Mukhopadhyay, Oscillator representation of the BCFT construction of D-branes in vacuum string field theory, JHEP 12 (2001) 025 [hep-th/0110136] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  79. [79]
    C.G. Callan, I.R. Klebanov, A.W.W. Ludwig and J.M. Maldacena, Exact solution of a boundary conformal field theory, Nucl. Phys. B 422 (1994) 417 [hep-th/9402113] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  80. [80]
    M. Kudrna, M. Rapcak and M. Schnabl, Ising model conformal boundary conditions from open string field theory, arXiv:1401.7980 [INSPIRE].
  81. [81]
    D. Takahashi, The boundary state for a class of analytic solutions in open string field theory, JHEP 11 (2011) 054 [arXiv:1110.1443] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  82. [82]
    T. Masuda, T. Noumi and D. Takahashi, Constraints on a class of classical solutions in open string field theory, JHEP 10 (2012) 113 [arXiv:1207.6220] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  83. [83]
    T. Masuda, Comments on new multiple-brane solutions based on Hata-Kojita duality in open string field theory, JHEP 05 (2014) 021 [arXiv:1211.2649] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  84. [84]
    H. Hata and T. Kojita, Winding number in string field theory, JHEP 01 (2012) 088 [arXiv:1111.2389] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  85. [85]
    H. Hata and T. Kojita, Singularities in K-space and multi-brane solutions in cubic string field theory, JHEP 02 (2013) 065 [arXiv:1209.4406] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  86. [86]
    H. Hata and T. Kojita, Inversion symmetry of gravitational coupling in cubic string field theory, JHEP 12 (2013) 019 [arXiv:1307.6636] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  87. [87]
    E. Aldo Arroyo, Multibrane solutions in cubic superstring field theory, JHEP 06 (2012) 157 [arXiv:1204.0213] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  88. [88]
    E. Aldo Arroyo, Comments on multibrane solutions in cubic superstring field theory, PTEP 2014 (2014) 063B03 [arXiv:1306.1865] [INSPIRE].MATHGoogle Scholar
  89. [89]
    R. Gopakumar, S. Minwalla and A. Strominger, Noncommutative solitons, JHEP 05 (2000) 020 [hep-th/0003160] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  90. [90]
    L. Rastelli, A. Sen and B. Zwiebach, String field theory around the tachyon vacuum, Adv. Theor. Math. Phys. 5 (2002) 353 [hep-th/0012251] [INSPIRE].MathSciNetCrossRefMATHGoogle Scholar
  91. [91]
    L. Rastelli, A. Sen and B. Zwiebach, Half strings, projectors and multiple D-branes in vacuum string field theory, JHEP 11 (2001) 035 [hep-th/0105058] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  92. [92]
    D.J. Gross and W. Taylor, Split string field theory. 1, JHEP 08 (2001) 009 [hep-th/0105059] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  93. [93]
    D. Gaiotto, L. Rastelli, A. Sen and B. Zwiebach, Star algebra projectors, JHEP 04 (2002) 060 [hep-th/0202151] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  94. [94]
    A. Jeffrey and D. Zwillinger, Table of integrals, series, and products, Academic Press, U.S.A. (2007).Google Scholar

Copyright information

© The Author(s) 2014

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical PhysicsMunichGermany
  2. 2.Dipartimento di FisicaUniversità di Torino and INFN — Sezione di TorinoTorinoItaly
  3. 3.Institute of Physics of the ASCR, v.v.i.Prague 8Czech Republic

Personalised recommendations