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

]|ˆ3

2ˆ|ˆ[4

1222

0

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

QQ

QQQ̂

B

BB Q

QQ

0

0ˆ

]|ˆ3

2ˆ|ˆ[4

1222

0

AAAYAAYTrg

S Q

)(

)()( 221

iQ

dzzbicQ

even

iodd

Structure of new Q

)()(

)()(

)()()(

1

2211

iiQ

iiQ

dzzbicicQ

even

ieven

iiodd

BRST

BRST

Q

QQ

0

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

QQ

QQQ

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(

02

1exp

srsr SNS

))'(),(('2

'

2Srs

ffs

i

d

i

d 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 2

0

2/12

ovdi nn )(2 12

0

2/112

0)))(()((2

)))(()((2

1

2

1exp

)()()()(

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