1. Tachyon condensation and Vacuum SuperString Field Theory
I.Ya. Aref'eva
Steklov Mathematical Institute
Why String Field Theory?
main motivations:
invariance principle behind string interactions
non-perturbative phenomenology
String Field Theory and Noncommutative Geometry
Tachyon Condensation in SSFT (Goldstone Phenomenon )
Closed string excitations
Massless particles
Vacuum SuperString Field Theory
Special solutions - sliver, lump, etc.

2. String Field Theory = Second Quantized String Theory
Infinite number of local fields
String Field A[X(σ)] - functional, or state in Fock space
Local space-time fields
Ghosts A[X(σ), c(σ), b (σ)]
Examples:

3. ? INTERACTION? GOAL Associative Product of String Fields
Examples of associative multiplications:
Pointwise multiplication of functions
Multiplication of matrices
Moyal product

4. Witten’s String Product
Coordinate representation

6. Multiplication in Vertex Language
Bilinear form
<A| B> = <V2| A> |B>
Multiplication
1’23 <V3 | = 423 <V3 |V2>41

7. Star Product
Three-string vertex

8. Moyal product in terms of vertices
M.Douglas, H.Liu, G.Moore, B.Zwiebach,hep-th/
Pointwise product

9. Diagonal basis
Matter vertex