in collaboration with y. baba(tsukuba) and k. murakami(kek)
DESCRIPTION
D-branes and Closed String Field Theory. N. Ishibashi (University of Tsukuba). In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK). JHEP 05(2006):029 JHEP 05(2007):020 JHEP 10(2007):008. Progress of String Theory and Quantum Field Theory - PowerPoint PPT PresentationTRANSCRIPT
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In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK)
JHEP 05(2006):029JHEP 05(2007):020JHEP 10(2007):008
D-branes and Closed String Field Theory
N. Ishibashi (University of Tsukuba)
Progress of String Theory and Quantum Field Theory Friday 7th December - Monday 10th December 2007 @ Media Center, Osaka City University
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• D-branes can be realized as soliton solutions in
open string field theory
• D-branes in closed string field theory?
Hashimoto and Hata
♦HIKKO♦A gauge invariant source term♦tension of the brane cannot be fixed
§1 Introduction
D-branes in string field theory
A.Sen,………
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For noncritical strings, the situation is better
c=0 noncritical strings
+ +double scalinglimit
String Field l
Describing the matrix model in terms of this field, we obtain the string field theory for c=0 noncritical strings
Kawai, N.I.
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joining-splitting interactions
Stochastic quantization of the matrix model Jevicki and Rodrigues
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correlation functions
Virasoro constraintsFKN, DVV
Virasoro constraints Schwinger-Dyson equationsfor the correlation functions
various vacua~
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Solitonic operators Fukuma and Yahikozawa
From one solution to the Virasoro constraint, one can generate another by the solitonic operator.
Hanada, Hayakawa, Kawai, Kuroki, Matsuo, Tada and N.I.
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These solitonic operators correspond to D-branes
state with D(-1)-brane ghost D-brane (Okuda and Takayanagi)
=
amplitudes with ZZ-branes are reproduced
the tension of the brane is fixed correctly
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critical strings?
noncritical case is simple
idempotency equation Kishimoto, Matsuo, Watanabe
For boundary states, things may not be so complicated
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We will show that
・ for OSp invariant SFT for the critical bosonic strings
・ we can construct BRS invariant observables using the boundary states for D-branes
imitating the construction of the solitonic operators for the noncritical string case.
Plan of the talk
§2 OSp Invariant String Field Theory
§3 D-brane States
§4 Conclusion and Discussion
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§2 OSp Invariant String Field Theory
light-cone gauge SFT
SO(25,1) symmetry
OSp invariant SFT =light-cone SFT withGrassmann
OSp(27,1|2) symmetrySiegel, Uehara, Neveu, West,Zwiebach, Kugo, Kawano,….
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variables
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action
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OSp theory 〜 covariant string theory with extra time and length
HIKKO
・ no
・ extra variables
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BRS symmetry
the string field Hamiltonian is BRS exact
The “action” cannot be considered as the usual action
looks like the action for stochastic quantization
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・ string length ・ joining-splitting interaction ・ extra time variable etc.
similar to noncriticalSFT
Green’s functions of BRS invariant observables = Green’s functions in 26D
S-matrix elements in 26D
∥
S-matrix elements derived from the light-cone gauge SFT
different from the usual formulation, but
One can show
Wick rotation, LSZ
We may be able to construct something like
Baba, Murakami, N.I.
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light-cone quantization
§3 D-brane States
Let us construct second quantized BRS invariant states, imitating the construction of the solitonic operator in the noncritical case.
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states with one soliton
will be fixed by requiring
c.f.
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Boundary states in OSp theory
boundary state for a flat Dp-brane
BRS invariant regularization
It is straightforward to include constant
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shorthand notation
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Idempotency equations
leading order in
Kishimoto, Matsuo, Watanabe
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Using these relations we obtain
if
Later we will show
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States with N solitons
Imposing the BRS invariance, we obtain
looks like a matrix model
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can be identified with the open string tachyon
may be identified with the eigenvalues
of the matrix valued tachyon
open string tachyon
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More generally we obtain
・ we can also construct
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amplitudes
saddle point approximation
generate boundaries on the worldsheet
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We have checked that the disk and cylinder amplitudes are reproduced correctly.
etc.
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§4 Conclusion and Discussion
♦similar construction for superstrings
♦other amplitudes
we need to construct OSp SFT for superstrings
♦D-brane ~ BRS invariant source term coherent state
♦more fundamental formulation?
♦ lower order in
contact term?
Yoneya