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Rolling Tachyon and Vacuum SuperString Field Theory

Rolling Tachyon and Vacuum SuperString Field Theory. I.Ya. A ref'eva Steklov Mathematical Institute. Based on : I. A. , D. Belov , A.Giryavets, A.Koshelev , hep-th/0112214, hep-th/ 0201197 , hep-th/0203227 , hep-th/0204239. and .

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Rolling Tachyon and Vacuum SuperString Field Theory

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  1. Rolling Tachyon and Vacuum SuperString Field Theory I.Ya. Aref'eva Steklov Mathematical Institute Based on : I.A., D. Belov, A.Giryavets, A.Koshelev, hep-th/0112214, hep-th/0201197, hep-th/0203227, hep-th/0204239 and

  2. i)Field theory (anharmonic oscillator) • corrections • p-adic strings • SFT OUTLOOK • Cubic SSFT action • Tachyon Condensation in SSFT • RollingTachyon • Vacuum SuperString Field Theory • i)New BRST charge • Special solutions - sliver, lump, etc.: • algebraic; surface states; Moyal representation • iii) Time dependence • Conclusion

  3. V Tachyon Condensation in SFT • Bosonic String - Tachyon • Tachyon Condensation inSFT • Level truncation Kostelecky,Samuel (1989) • Tachyon inGSO( - ) sector of NS string

  4. I.A., Medvedev, Zubarev (1990) Preitschopf, Thorn,Yost (1990) String Field Theory on a non-BPS brane I.A.,Belov,Koshelev,Medvedev(2001) E.Witten (1986)

  5. Level GSO Name Picture -1 Picture 0 0 + u - 1/2 - t 1 + r 3/2 - s 2 + I.A., Belov, Koshelev, P.M. (2001) Vertex operators in pictures –1 and 0 Berkovits (1995) N.B.,Sen,Zwiebach (2000)

  6. Tachyon Condensation in SSFT

  7. FAQ:cubic unbounded A.:Auxiliary fields u, t fields

  8. SFT Sen’s conjecture (1999) Vacuum Energy = Brane Tension Strings Branes

  9. = NO OPEN STRING EXCITATIONS CLOSED STRING EXCITATIONS Sen’s conjectures (1999) 97.5% Our calculations: 105.8%

  10. RollingTachyon • Anharmonic oscillator • Alpha ‘ corrections • p-adic strings • SFT (for bosonic string Sen,hep-th/0203211) • SSFT for non-BPS branes

  11. Anharmonic oscillator If resonance i.e.

  12. Two regimes: Rolling Tachyon Initial condition near the top Initial condition near the bottom

  13. Rolling Tachyon (bosonic case) Initial condition near the top Initial condition near the bottom

  14. Alpha ‘ corrections (boson case) • First order Solutions

  15. Alpha ‘ corrections (non-BPS case) • First order Solutions

  16. Siegel gauge Usual pert.theory Resonance -- + + … Problems!!! Solutions to SFT E.O.M. = Sen,hepth/020715

  17. NS sector No picture changing operator Problems!!! defines the fold AMZ,1990 Solutions to SSFT E.O.M.

  18. NO OPEN STRING EXCITATIONS VSFT

  19. Vacuum String Field Theory on a non-BPS brane I.A., Belov, Giryavets (2002)

  20. solution to E.O.M Structure of new Q SFT in the background field Ohmori

  21. Tests Solution to VSFT E.O.M

  22. E.O.M. Analog of Noncommutative Soliton in Strong Coupling Limit Gopakumar, Minwalla,Strominger

  23. Methods of solving • Algebraic method • Surface states method • Moyal representation I.Bars,M.Douglas,G.Moore • Half-strings

  24. Bosonic sliver Rastelli, Sen, Zwiebach; Kostelecky, Potting... Algebraic Method Identities for squeezed states I.A., Giryavets, Medvedev; Marino, Schiappa

  25. Twisted SuperSliver • Superghost twisted sliver • Superghost twisted sliver equation • Sliver with insertion • Picture changing

  26. Sliver in the Moyal representation Identity Sliver

  27. Conclusion • What we know • What we get • Open problems

  28. What we have got in cubic SSFT Tachyon condensation Rolling tachyon near the top Vacuum SSFT andsome solutions

  29. What we know SFT proposes a hard, but a surmountable way to get answers concerning non-perturbative phenomena Two sets of basis: i) related with spectrum offree string ii) related with "strong coupling “ regime (may be suitable for study VSFT)

  30. More tests for checking validity of VSSFT Other solutions (lump, kink solutions); especially with time dependence Use the Moyal basis to construct the tachyon condensate and other solutions Classification of projectors in open string field algebra and its physical meaning Closed string excitations in VSSFT Open Problems

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