Tachyon condensation and Vacuum SuperString Field Theory

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Presentation transcript:

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.

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:

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

Witten’s String Product Coordinate representation

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

Star Product Three-string vertex

Moyal product in terms of vertices M.Douglas, H.Liu, G.Moore, B.Zwiebach,hep-th/0202087 Pointwise product

Diagonal basis Matter vertex