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Democratic superstring field theory: gauge fixing

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Abstract

We show that a partial gauge fixing of the NS sector of the democratic-picture superstring field theory leads to the non-polynomial theory. Moreover, by partially gauge fixing the Ramond sector we obtain a non-polynomial fully RNS theory at pictures 0 and \( \frac{1}{2} \). Within the democratic theory and in the partially gauge fixed theory the equations of motion of both sectors are derived from an action. We also discuss a representation of the non-polynomial theory analogous to a manifestly two-dimensional representation of WZW theory and the action of bosonic pure-gauge solutions.

We further demonstrate that one can consistently gauge fix the NS sector of the democratic theory at picture number −1. The resulting theory is new. It is a \( {\mathbb{Z}_2} \) dual of the modified cubic theory. We construct analytical solutions of this theory and show that they possess the desired properties.

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References

  1. A. Sen, Descent relations among bosonic D-branes, Int. J. Mod. Phys. A 14 (1999) 4061 [hep-th/9902105] [SPIRES].

    ADS  Google Scholar 

  2. A. Sen, Universality of the tachyon potential, JHEP 12 (1999) 027 [hep-th/9911116] [SPIRES].

    Article  ADS  Google Scholar 

  3. E. Fuchs and M. Kroyter, Analytical solutions of open string field theory, arXiv:0807.4722 [SPIRES].

  4. M. Schnabl, Algebraic solutions in open string field theory — a lightning review, arXiv:1004.4858 [SPIRES].

  5. M. Kroyter, Superstring field theory in the democratic picture, arXiv:0911.2962 [SPIRES].

  6. D. Friedan, E.J. Martinec and S.H. Shenker, Conformal invariance, supersymmetry and string theory, Nucl. Phys. B 271 (1986) 93 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  7. G.T. Horowitz, R.C. Myers and S.P. Martin, BRST cohomology of the superstring at arbitrary ghost number, Phys. Lett. B 218 (1989) 309 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  8. B.H. Lian and G.J. Zuckerman, BRST cohomology of the supervirasoro algebras, Commun. Math. Phys. 125 (1989) 301 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. N. Berkovits and C. Vafa, N = 4 topological strings, Nucl. Phys. B 433 (1995) 123 [hep-th/9407190] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  10. N. Berkovits, A new description of the superstring, hep-th/9604123 [SPIRES].

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

    Article  MathSciNet  ADS  Google Scholar 

  12. N. Berkovits, Super-Poincaré invariant superstring field theory, Nucl. Phys. B 450 (1995) 90 [hep-th/9503099] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. I.Y. Arefeva, P.B. Medvedev and A.P. Zubarev, Background formalism for superstring field theory, Phys. Lett. B 240 (1990) 356 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  14. I.Y. Arefeva, P.B. Medvedev and A.P. Zubarev, New representation for string field solves the consistency problem for open superstring field theory, Nucl. Phys. B 341 (1990) 464 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. C.R. Preitschopf, C.B. Thorn and S.A. Yost, Superstring field theory, Nucl. Phys. B 337 (1990) 363 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. M. Kroyter, Superstring field theory equivalence: Ramond sector, JHEP 10 (2009) 044 [arXiv:0905.1168] [SPIRES].

    ADS  Google Scholar 

  17. N. Berkovits, The Ramond sector of open superstring field theory, JHEP 11 (2001) 047 [hep-th/0109100] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. Y. Michishita, A covariant action with a constraint and Feynman rules for fermions in open superstring field theory, JHEP 01 (2005) 012 [hep-th/0412215] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  19. N. Berkovits, Relating the RNS and pure spinor formalisms for the superstring, JHEP 08 (2001) 026 [hep-th/0104247] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. M. Kroyter, On string fields and superstring field theories, JHEP 08 (2009) 044 [arXiv:0905.1170] [SPIRES].

    ADS  Google Scholar 

  21. E. Witten, Noncommutative geometry and string field theory, Nucl. Phys. B 268 (1986) 253 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  22. N. Berkovits, A. Sen and B. Zwiebach, Tachyon condensation in superstring field theory, Nucl. Phys. B 587 (2000) 147 [hep-th/0002211] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  23. M. Kroyter, Comments on superstring field theory and its vacuum solution, JHEP 08 (2009) 048 [arXiv:0905.3501] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  24. M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, Princeton U.S.A. (1992) [SPIRES].

    MATH  Google Scholar 

  25. P.-J. De Smet and J. Raeymaekers, The tachyon potential in Witten’s superstring field theory, JHEP 08 (2000) 020 [hep-th/0004112] [SPIRES].

    Article  Google Scholar 

  26. I.Y. Arefeva, D.M. Belov and A.A. Giryavets, Construction of the vacuum string field theory on a non-BPS brane, JHEP 09 (2002) 050 [hep-th/0201197] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  27. I.Y. Aref’eva, A.S. Koshelev, D.M. Belov and P.B. Medvedev, Tachyon condensation in cubic superstring field theory, Nucl. Phys. B 638 (2002) 3 [hep-th/0011117] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  28. S.J. Gates, M.T. Grisaru, M. Roček and W. Siegel, Superspace, or one thousand and one lessons in supersymmetry, Front. Phys. 58 (1983) 1 [hep-th/0108200] [SPIRES].

    Google Scholar 

  29. G.T. Horowitz, J.D. Lykken, R. Rohm and A. Strominger, A purely cubic action for string field theory, Phys. Rev. Lett. 57 (1986) 283 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. N. Berkovits, Y. Okawa and B. Zwiebach, WZW-like action for heterotic string field theory, JHEP 11 (2004) 038 [hep-th/0409018] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. E. Witten, Nonabelian bosonization in two-dimensions, Commun. Math. Phys. 92 (1984) 455 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. M. Henneaux, Lectures on the antifield-BRST formalism for gauge theories, Nucl. Phys. Proc. Suppl. 18A (1990) 47 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. J. Gomis, J. Paris and S. Samuel, Antibracket, antifields and gauge theory quantization, Phys. Rept. 259 (1995) 1 [hep-th/9412228] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. M. Schnabl, Comments on marginal deformations in open string field theory, Phys. Lett. B 654 (2007) 194 [hep-th/0701248] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  35. 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].

    Article  MathSciNet  ADS  Google Scholar 

  36. T. Erler, Marginal solutions for the superstring, JHEP 07 (2007) 050 [arXiv:0704.0930] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  37. Y. Okawa, Analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 084 [arXiv:0704.0936] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  38. Y. Okawa, Real analytic solutions for marginal deformations in open superstring field theory, JHEP 09 (2007) 082 [arXiv:0704.3612] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Kling, O. Lechtenfeld, A.D. Popov and S. Uhlmann, Solving string field equations: new uses for old tools, Fortsch. Phys. 51 (2003) 775 [hep-th/0212335] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. E. Fuchs and M. Kroyter, On the classical equivalence of superstring field theories, JHEP 10 (2008) 054 [arXiv:0805.4386] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  41. E. Fuchs, M. Kroyter and R. Potting, Marginal deformations in string field theory, JHEP 09 (2007) 101 [arXiv:0704.2222] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  42. E. Fuchs and M. Kroyter, Marginal deformation for the photon in superstring field theory, JHEP 11 (2007) 005 [arXiv:0706.0717] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  43. M. Kiermaier and Y. Okawa, Exact marginality in open string field theory: a general framework, JHEP 11 (2009) 041 [arXiv:0707.4472] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  44. M. Kiermaier and Y. Okawa, General marginal deformations in open superstring field theory, JHEP 11 (2009) 042 [arXiv:0708.3394] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  45. M. Kiermaier, Y. Okawa and P. Soler, Solutions from boundary condition changing operators in open string field theory, arXiv:1009.6185 [SPIRES].

  46. A. Recknagel and V. Schomerus, Boundary deformation theory and moduli spaces of D-branes, Nucl. Phys. B 545 (1999) 233 [hep-th/9811237] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. M. Schnabl, Analytic solution for tachyon condensation in open string field theory, Adv. Theor. Math. Phys. 10 (2006) 433 [hep-th/0511286] [SPIRES].

    MathSciNet  MATH  Google Scholar 

  48. 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].

    Article  MathSciNet  ADS  Google Scholar 

  49. E. Fuchs and M. Kroyter, On the validity of the solution of string field theory, JHEP 05 (2006) 006 [hep-th/0603195] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  50. I. Ellwood and M. Schnabl, Proof of vanishing cohomology at the tachyon vacuum, JHEP 02 (2007) 096 [hep-th/0606142] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  51. L. Bonora, C. Maccaferri and D.D. Tolla, Relevant deformations in open string field theory: a simple solution for lumps, arXiv:1009.4158 [SPIRES].

  52. T. Erler, Tachyon vacuum in cubic superstring field theory, JHEP 01 (2008) 013 [arXiv:0707.4591] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  53. T. Erler, Split string formalism and the closed string vacuum, JHEP 05 (2007) 083 [hep-th/0611200] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. T. Erler, Split string formalism and the closed string vacuum. II, JHEP 05 (2007) 084 [hep-th/0612050] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  55. 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].

    Article  MathSciNet  Google Scholar 

  56. R.V. Gorbachev, New solution of the superstring equation of motion, Theor. Math. Phys. 162 (2010) 90 [SPIRES].

    Article  MathSciNet  MATH  Google Scholar 

  57. 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].

    MathSciNet  ADS  Google Scholar 

  58. T. Erler and M. Schnabl, A simple analytic solution for tachyon condensation, JHEP 10 (2009) 066 [arXiv:0906.0979] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  59. I. Ellwood, B. Feng, Y.-H. He and N. Moeller, The identity string field and the tachyon vacuum, JHEP 07 (2001) 016 [hep-th/0105024] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  60. N. Berkovits, Pure spinor formalism as an N = 2 topological string, JHEP 10 (2005) 089 [hep-th/0509120] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  61. N. Berkovits and W. Siegel, Regularizing cubic open Neveu-Schwarz string field theory, JHEP 11 (2009) 021 [arXiv:0901.3386] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  63. B. Zwiebach, Interpolating string field theories, Mod. Phys. Lett. A 7 (1992) 1079 [hep-th/9202015] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  64. B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Y. Aisaka, E.A. Arroyo, N. Berkovits and N. Nekrasov, Pure spinor partition function and the massive superstring spectrum, JHEP 08 (2008) 050 [arXiv:0806.0584] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  66. O.A. Bedoya and N. Berkovits, GGI lectures on the pure spinor formalism of the superstring, arXiv:0910.2254 [SPIRES].

  67. M. Kroyter, Analytical solutions of pure-spinor superstring field theory, to be published.

  68. F. Bursa and M. Kroyter, Lattice string field theory, PoS(Lattice 2010)047 [arXiv:1009.4414] [SPIRES].

  69. N. Berkovits, M.T. Hatsuda and W. Siegel, The big picture, Nucl. Phys. B 371 (1992) 434 [hep-th/9108021] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  70. M. Kiermaier, Y. Okawa and B. Zwiebach, The boundary state from open string fields, arXiv:0810.1737 [SPIRES].

  71. T. Erler, Exotic universal solutions in cubic superstring field theory, arXiv:1009.1865 [SPIRES].

  72. R. Saroja and A. Sen, Picture changing operators in closed fermionic string field theory, Phys. Lett. B 286 (1992) 256 [hep-th/9202087] [SPIRES].

    MathSciNet  ADS  Google Scholar 

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Kroyter, M. Democratic superstring field theory: gauge fixing. J. High Energ. Phys. 2011, 81 (2011). https://doi.org/10.1007/JHEP03(2011)081

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