ii summer school in modern mathematical physics september 1-12, 2002 kopaonik, (serbia) yugoslavia
DESCRIPTION
Super. String Field Theory. I.Ya. A ref'eva Steklov Mathematical Institute. (Cubic SSFT). (Lecture II). II SUMMER SCHOOL IN MODERN MATHEMATICAL PHYSICS September 1-12, 2002 Kopaonik, (SERBIA) YUGOSLAVIA. String Field Theory. L.Bonora. OUTLOOK. SuperString Field Theory. - PowerPoint PPT PresentationTRANSCRIPT
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