2. 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

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

4. Tachyon Condensation in SFT Bosonic String - Tachyon Tachyon Condensation in SFT Tachyon in GSO ( - ) sector of NS string Level truncation V Kostelecky,Samuel (1989)

5. String Field Theory on a non-BPS brane I.A.,Belov,Koshelev,Medvedev(2001) Parity GSO odd + even - E.Witten (1986) I.A., Medvedev, Zubarev (1990) Preitschopf, Thorn, Yost (1990)

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

7. Tachyon Condensation in SSFT

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

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

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

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

12. Anharmonic oscillator If resonance i.e.

13. Rolling Tachyon Initial condition near the topInitial condition near the bottom Two regimes:

14. Rolling Tachyon ( bosonic case ) Initial condition near the topInitial condition near the bottom

15. Alpha ‘ corrections (boson case) First order Solutions

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

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

18. Solutions to SSFT E.O.M. No picture changing operator NS sector Problems!!! defines the foldAMZ,1990

19. NO OPEN STRING EXCITATIONS VSFT

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

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

22. Tests Solution to VSFT E.O.M

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

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

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

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

27. Sliver in the Moyal representation Identity Sliver

28. Conclusion What we know What we get Open problems

29. What we have got in cubic SSFT Tachyon condensation Rolling tachyon near the top Vacuum SSFT and some solutions

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

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