Upload
avis-summers
View
219
Download
0
Embed Size (px)
Citation preview
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)
M M’
M
M’
M M’
M M’
M
M’
M
M’
Wedge States
Star Multiplication of Wedge States
=
Conformal SliverConformal map
Comparison with algebraic sliver
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
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
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