Tachyon condensation and Vacuum SuperString Field Theory

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Super
String Field Theory
and Vacuum Super
String Field Theory
II SUMMER SCHOOL INMODERN
MATHEMATICAL PHYSICS September 1-12,
2002Kopaonik, (SERBIA) YUGOSLAVIA
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• Why

String Field Theory?
main motivations gauge invariance
principle behind string interactions
non-perturbative phenomena

• What

we can calculate in String Field Theory?
(analog of Higgs and Goldstone Phenomena)
Condensation of Tachyon
Brane tensions
Rolling Tachyon

• How

we can do calculations in SFT?

String Field Theory and Noncommutative Geometry

String Field Theory and CFT
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String Field Theory ?Second Quantized String
Theory

• Infinite number of local fields

• String Field AX(s) - functional, or state
  in Fock space

• Ghosts AX(s), c(s), b (s)

• Example

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INTERACTION ?

Associative Product of String Fields
Examples of associative multiplications

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Wittens String Product
Associative Product of String Fields --
Coordinate representation
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(No Transcript)
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SFT Action
E.Witten (1986)
Gauge transformations
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SFT Action is given
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Tachyon Condensation in SFT

• Bosonic String - Tachyon

Kostelecky,Samuel (1989)
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Sens conjecture (1999)
Brane Tension

Vacuum Energy
Strings
Branes
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Sens conjectures (1999)
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Rolling Tachyon
Motivationscosmology,...

• Anharmonic oscillator
• alpha corrections
• p-adic strings

I.Volovich(1987) P.Frampton, Nishino(1988) Brekk
e,Freund,Witten(1988), I.A,B.Dragovic,I.Volovich(1
988)
Moeller, Zwiebach, hep-th/0207107
p-adic and NC space-time
I.A.,I.Volovich, 1990
Sen, Strings2002

• SFT

I.A, A.Giryavets, A.Koshelev
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Rolling Tachyon
Spatially homogeneous field configurations
E.O.M.
where
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Rolling Tachyon
Anharmonic oscillator approximation
E.O.M.
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Anharmonic oscillator
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Rolling Tachyon
Initial condition near the top
Initial condition near the bottom
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Rolling Tachyon (bosonic case)
Initial condition near the top
Initial condition near the bottom
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Alpha corrections (boson case)

• First order

Solutions
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Rolling Tachyon
E.O.M.
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Rolling Tachyon
E.O.M. X-dependence
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Rolling Tachyon
E.O.M.
Two analogues
i) p-adic strings
ii) non-commutative solitons in strong coupling
regime
Gopakumar, Minwalla,Strominger
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Rolling Tachyon
Time evolution in the sliver-tachyon and p-adic
strings
p2,3,5,..
()
There is no solution such that
with
BUT this contradiction does not take place for ()
decreasing monotonically in time
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Solutions to SFT E.O.M.
Analog of Yang-Feldman eq.
Resonance

Sen
Problems!!!
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OUTLOOK
String Field Theory
L.Bonora
Noncommutative Field Theories and (Super) String
Field Theories, hep-th/0111208, I.A., D. Belov,
A.Giryavets, A.Koshelev,P.Medvedev
SuperString Field Theory

• Cubic SSFT action

2-nd

• Tachyon Condensation in SSFT

• Rolling Tachyon

3-d

• Vacuum SuperString Field Theory

i) New BRST charge ii) Special solutions -
sliver, lump, etc. algebraic surface
states Moyal representation