II SUMMER SCHOOL INII SUMMER SCHOOL INMODERN MATHEMATICAL PHYSICSMODERN MATHEMATICAL PHYSICS

September 1-12, 2002Kopaonik, (SERBIA) YUGOSLAVIA

Super String Field Theory

I.Ya. Aref'evaSteklov Mathematical Institute

(Lecture II)

(Cubic SSFT)

OUTLOOK

i) New BRST chargeii) Special solutions - sliver, lump, etc.: algebraic; surface states; Moyal representation

• Cubic SSFT action

• Vacuum SuperString Field Theory

• Tachyon Condensation in SSFT

• Rolling Tachyon

String Field Theory L.Bonora

SuperString Field Theory

2-nd

3-d

1-st

Super String Theory (NSR-formalism)

]22

1[

2

1

02

iXXddS

2dim Majorana spinor, 0T

01

100

0

01

i

i

Super String Theory (NSR-formalism)

Super String Theory (NSR-formalism)

),(),( zz

][2

1 22

zdS f

rn

nn

zz 2/1)(

r=1/2 for R-sector; r=0 for NS-sector

Quantization

Correlators

0,, mnmn

wzwz

1

2)()(

Identity Overlap

Three string vertex overlapThree string vertex overlap

Gross, Jevicki

Fermionic Vertices

Identity

Three string vertex

Superstring (NSR-formalism); ghosts

zdSgh2

2

1

rn

nn

zz 2/1)(

r=1/2 for R-sector; r=0 for NS-sector

Quantization 0,],[ mnnm

rn

nn

zz 2/3)(

Bosonization e e02 e

Cubic Super String Field Theory

]|3

2[

4

120

AAAXQAAg

SE.Witten (1986)

I.A., Medvedev, Zubarev (1990)Preitschopf, Thorn, Yost (1990)2Y

]|3

2|[

4

1222

0

AAAYQAAYg

S

Went,….

PROBLEMS E.O.M. 0 AXAQA

0 AAQA Up to a kernal

String Field Theory on a non-BPS brane

I.A.,Belov,Koshelev,Medvedev(2001)

3ˆ BQQ

]|ˆ3

2ˆ|ˆ[4

1222

0

AAAYAQAYTrg

S

23 iAAA

Parity GSO odd +

even -A

A

Tachyon Condensation in SFT

• Bosonic String - Tachyon

• Super String has no Tachyon

• Tachyon in GSO ( - ) sector of NS string

• Level truncation

V

it

Kostelecky,Samuel (1989)

Vertex operators in pictures –1 and 0

Berkovits,Sen,Zwiebach (2000)

)(z

I.A.,Belov,Koshelev,Medvedev(2001)

6,...1,,, ivtu i

+2

s-3/2

r+1

t-1/2

-u+0

Picture 0Picture -1NameGSOLevel10 L F)1(

iv

ce

2 ecc

ec

22

,,

cec

ceTF

c

e cc,

eebcecTF ,),(,

eTccT

cTcTc

F

B

,,

,,,2

2

Tachyon Condensation in SSFT

242/12

0

)1(

4

1

1024

811tt

gV p

242/12

0

)4(

4

1

69120

50531tt

gV

p

257.1)1( ct

308.1)4( ct

For the non-polinomial Berkovic action (Berkovic,Sen, Zwiebach):

85%, 90.5%

97.5%

105%

FAQ: cubic unbounded 24

A.: Auxiliary fields

23

222 )( ag )(21 222 ag

u, t fields

]3

1

4

1[

1 22

222/12

0

)1( uttug

Lp

33

4

242/12

0

)1(

4

1

1024

811tt

gV p

NO OPEN STRING EXCITATIONS

VSFT