Surface States Global coordinates Local coordinate Surface state is a bra = lim.

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Surface States Global coordinates Local coordinate Surface state is a bra <Σ| associated to a Riemann surface Σ r any local operator Φ(ξ) | Φ>= lim Φ(ξ)|0> ξ→0 < Σ |Φ >= <s ○ Φ(0) >D h s ○ Φ(0) = (s’ (0)) Φ(s(0)) m : ξ → u =s(ξ)

Transcript of Surface States Global coordinates Local coordinate Surface state is a bra = lim.

Page 1: Surface States Global coordinates Local coordinate Surface state is a bra = lim.

Surface StatesGlobal coordinates

Local coordinate

Surface state is a bra <Σ| associated to a Riemann surface Σ

For any local operator Φ(ξ) ↔ | Φ>= lim Φ(ξ)|0> ξ→0

< Σ |Φ >= <s ○ Φ(0) >D

h

s ○ Φ(0) = (s’ (0)) Φ(s(0))

m : ξ → u =s(ξ)

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M M’

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M

M’

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M M’

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M M’

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M

M’

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M

M’

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Wedge States

Star Multiplication of Wedge States

=

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Conformal SliverConformal map

Comparison with algebraic sliver

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What we know

Two sets of basis: i) related with spectrum of free string ii) related with "strong coupling" regime (may be suitable for study VSFT

Identity and Sliver in Moyal Basis

Identity

Sliver

SFT proposes a hard, but a surmountable way to get answers concerning non- perturbative phenomena

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Open Problems

More tests for checking validity of VSSFT

Use the Moyal basis to construct the tachyon condensate and othersolutions

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 VSFT

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References:• I.Ya.~Aref'eva, D.M.~Belov, A.S.~Koshelev and

P.B.~Medvedev,Tachyon Condensation in the Cubic Superstring Field Theory, Nucl.Phys., hep-th/0011117;

• Gauge invariance and tachyon condensation in cubic superstring field theory, Nucl.Phys., hep-th/010719

• I.Ya.Aref'eva, A.A.Giryavets and A.S.Koshelev,NS Ghost Slivers, Phys.Lett., hep-th/0203227

• I.Ya.Aref'eva, A.A.Giryavets and P.B.Medvedev,NS Matter Sliver, Phys.Lett.B 532 (2002) 291, hep-th/0112214;

• I.Ya.Aref'eva, A.A.Giryavets, Open Superstring Star as a Continuous Moyal Product Product, hep-th/0204164

• D.M.Belov, Diagonal Representation of Open String Star and Moyal

• I.Ya.Aref'eva, D.M.Belov and A.A.Giryavets,Construction of the Vacuum String Field Theory on a Non-BPS Brane, hep-th/0201197

• Noncommutative Field Theories and (Super)String Field Theories, hep-th/0111208