Tachyon condensation and Vacuum SuperString Field Theory

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(Lecture III)
Based on I.A., D. Belov, A.Giryavets,
A.Koshelev, hep-th/0112214,
hep-th/0201197,
hep-th/0203227, hep-th/0204239
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OUTLOOK

• Vacuum SuperString Field Theory

i) New BRST charge ii) Special solutions -
sliver, lump, etc. algebraic surface
states Moyal representation

• Conclusion

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Sens conjectures
0.975
Our calculations
1.058
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NO OPEN STRING EXCITATIONS
VSFT
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String Field Theory on a non-BPS brane
Parity GSO
odd
even -
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Vacuum String Field Theory on a non-BPS brane

• I.A., Belov, Giryavets (2002)

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Structure of new Q
SFT in the background field
Ohmori
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E.O.M.
Analog of Noncommutative Soliton in Strong
Coupling Limit
Gopakumar, Minwalla,Strominger
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Methods of solving

• Algebraic method

• Surface states method

• Moyal representation

• Half-strings

• Auxiliary linear system

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Algebraic Method
Identities for squeezed states
I.A., Giryavets, Medvedev Marino, Schiappa
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Conformal Sliver
Conformal map
Comparison with algebraic sliver
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Universality of Conformal Sliver

• Surface states

conformal vacuum

• Conformal definition of surface states

• Sliver conformal map

• Sliver projection equation

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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

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Sliver in the Moyal representation
Identity
Sliver
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Twisted SuperSliver

• Superghost twisted sliver

I.A., Giryavets,Koshelev, hep-th/0203227

• Superghost twisted sliver equation

• Sliver with insertion

• Picture changing

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Tests
Solution to VSFT E.O.M
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Conclusion

• What we know
• What we have got
• Open problems

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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 of free string
ii) related with "strong coupling regime
(may be suitable for study VSFT)
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Open Problems