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Vacuum SuperString Field Theory. I.Ya. A ref'eva Steklov Mathematical Institute. (Lecture III). Based on : I. A. , D. Belov , A.Giryavets, A.Koshelev , hep-th/0112214, hep-th/ 0201197 , hep-th/0203227 , hep-th/0204239. OUTLOOK. - PowerPoint PPT Presentation
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Vacuum SuperString Field Theory
I.Ya. Aref'evaSteklov Mathematical Institute
Based on : I.A., D. Belov, A.Giryavets, A.Koshelev, hep-th/0112214, hep-th/0201197, hep-th/0203227, hep-th/0204239
(Lecture III)
OUTLOOK
i) New BRST charge
ii) Special solutions - sliver, lump, etc.: algebraic; surface states; Moyal representation
• Vacuum SuperString Field Theory
• Conclusion
Sen’s conjectures
E braneT=
NO OPEN STRING EXCITATIONS
CLOSED STRING EXCITATIONS (?)
Our calculations:
0.975
1.058
NO OPEN STRING EXCITATIONS
VSFT
String Field Theory on a non-BPS brane
3ˆ BB QQ
]|ˆ32ˆ|ˆ[
41
2220
AAAYAQAYTrg
S B
23 iAAA
Parity GSO odd + even -
A
A
Vacuum String Field Theory on a non-BPS brane
I.A., Belov, Giryavets (2002)
23 iAAA
oddeven
evenodd
QQQQ
Q̂
B
BB Q
00ˆ
]|ˆ32ˆ|ˆ[
41
2220
AAAYAAYTrg
S Q
)(
)()( 221
iQ
dzzbicQ
even
iodd
Structure of new Q
)()(
)()(
)()()(1
2211
iiQ
iiQ
dzzbicicQ
even
ieven
iiodd
BRST
BRST
Q0
0
,...}{ 0AQBRST Q
solution to E.O.M0A
SFT in the background field
newQ redef.-fieldQ
A
A
000 , AAA
AAA 0
Ohmori
oddeven
evenodd
QQQQ
Q
E.O.M.
Analog of Noncommutative Soliton in Strong Coupling Limit
Gopakumar, Minwalla,Strominger
0 AAAQ 0 mmm AAA
Methods of solving
• Algebraic method
AAA
• Surface states method
• Moyal representation
• Half-strings
• Auxiliary linear system
Algebraic Method
I.A., Giryavets, Medvedev;Marino, Schiappa
Identities for squeezed states
Bosonic sliver Rastelli, Sen, Zwiebach; Kostelecky, Potting...
0
jiji aSae
Conformal SliverConformal map
Comparison with algebraic sliver
Universality of Conformal Sliver
)arctan()f(
021exp
srsr SNS
))'(),(('2
'2
Srs
ffs
id
id hshr
),();,(;;X cb
• Conformal definition of surface states
• Sliver conformal map
• Surface states 0,0fUS conformal vacuum
• Sliver projection equation
Open Superstring Star in Diagonal Basis
evd nn )(2 20
2/12
ovdi nn )(2 120
2/112
0)))(()((2
)))(()((21
21exp
)()()()(
0
)()()()(3
1,3
bababaab
bababaab
baV
eooei
ooeedNV
• Diagonal basis
• Three-string vertex in diagonal basis
• Identity and sliver in diagonal basis
0)(exp0
oejdiNI I 0)(exp
0
oeTdiN
4
tanh)( j
•Spectrum of identity and sliver
2exp)( T
I.A.,A.Giryavets hep-th/0204239
Sliver in the Moyal representation
Identity
Sliver
)1('))()(('' )()( ii eiceic
Twisted SuperSliver• Superghost twisted sliver
00'0'0' )0(1
ecUUbcfbcf
• Superghost twisted sliver equation
~))()((~~ ii
0,'000)0(0)(~))(( )0(1
ecUiYUiY
bcfbcf
• Sliver with insertion
• Picture changing
0)0(0~ bcfU
)1()()( iYiY
)()(
)()(
)()()(1
2211
iiQ
iiQ
dzzbicicQ
even
ieven
iiodd
I.A., Giryavets,Koshelev, hep-th/0203227
Tests
Solution to VSFT E.O.M
Conclusion
• What we know• What we have got• Open problems
What we know
Two sets of basis:
SSFT proposes a hard, but a surmountable way to get answers concerning non-perturbative phenomena
i) related with spectrum of free string
ii) related with "strong coupling “ regime (may be suitable for study VSFT)
What we have got in cubic SSFT
Tachyon condensation
Rolling tachyon near the top
Vacuum SSFT and some solutions
Open Problems
More tests for checking validity of VSSFT
Other solutions (lump, kink solutions); especially with time dependence
Classification of projectors in open string field algebra and its physical meaning
Use the Moyal basis to construct the tachyon condensate and other solutions
Closed string excitations in VSSFT