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Understanding Vacuum SuperString Field Theory: New Insights and Exciting Conjectures

This lecture series explores Vacuum SuperString Field Theory and its implications on open and closed string excitations. The presentation delves into new BRST charge developments, special solutions like sliver and lump states, as well as Sen’s conjectures with calculations and solutions in the background field. Methods such as algebraic, surface states, and Moyal representation are dissected along with the exploration of half-strings and auxiliary linear systems. The lecture covers topics on twisted slivers, conformal mapping, and superghost equations, offering insights into VSFT and SSFT solutions, tachyon condensation, and the classification of projectors in string field algebra. Open problems and future directions are also discussed to inspire further research endeavors.

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Understanding Vacuum SuperString Field Theory: New Insights and Exciting Conjectures

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

  2. OUTLOOK • Vacuum SuperString Field Theory i)New BRST charge ii) Special solutions - sliver, lump, etc.: algebraic; surface states; Moyal representation • Conclusion

  3. = NO OPEN STRING EXCITATIONS CLOSED STRING EXCITATIONS(?) Sen’s conjectures 0.975 Our calculations: 1.058

  4. NO OPEN STRING EXCITATIONS VSFT

  5. String Field Theory on a non-BPS brane

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

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

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

  9. Methods of solving • Algebraic method • Surface states method • Moyal representation • Half-strings • Auxiliary linear system

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

  11. Conformal Sliver Conformal map Comparison with algebraic sliver

  12. Surface states conformal vacuum Universality of Conformal Sliver • Conformal definition of surface states • Sliver conformal map • Sliver projection equation

  13. Open Superstring Star in Diagonal Basis I.A.,A.Giryavets hep-th/0204239 • Diagonal basis • Three-string vertex in diagonal basis • Identity and sliver in diagonal basis • Spectrum of identity and sliver

  14. Sliver in the Moyal representation Identity Sliver

  15. Twisted SuperSliver • Superghost twisted sliver I.A., Giryavets,Koshelev, hep-th/0203227 • Superghost twisted sliver equation • Sliver with insertion • Picture changing

  16. Tests Solution to VSFT E.O.M

  17. Conclusion • What we know • What we have got • Open problems

  18. What we know SSFT 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)

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

  20. 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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