d-branes and closed string field theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf ·...
TRANSCRIPT
![Page 1: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/1.jpg)
1
In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK)
hep-th/0603152 (JHEP 0605:029,2006 )hep-th/0702xxx
D-branes and Closed String Field Theory
N. Ishibashi (University of Tsukuba)
Komaba2007 Recent Developments in Strings and FieldsOn the occasion of T.Yoneya’s 60th birthday Feb. 11, 2007
![Page 2: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/2.jpg)
2
• D-branes can be realized as solitonsolutions in open string field theory
• D-branes in closed string field theory?
A.Sen,……….Okawa’s talk
Hashimoto and HataHIKKO
♦A BRS invariant source term♦c is arbitrary
§1 Introduction
D-branes in string field theory
![Page 3: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/3.jpg)
3
String Field l
String Field Theory~Collective Field Theory in MM
Jevicki andSakita
Kawai and N.I., Jevicki and Rodrigues
D-branes in SFT for noncritical strings
SFT for c=0
![Page 4: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/4.jpg)
4
joining-splitting interactions
loop amplitudes
Virasoro constraints FKN, DVV
![Page 5: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/5.jpg)
5
Solitonic operators
state with D(-1)-brane ghost D-brane
c.f.
Fukuma and YahikozawaHanada, Hayakawa, Kawai, Kuroki, Matsuo, Tada and N.I.
these solitonic operators reproduce amplitudes with ZZ-branes
![Page 6: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/6.jpg)
6
♦Can one construct such solitonic operators in SFT for critical strings?
Similar construction is possible for OSp invariantstring field theory
§2 OSp invariant string field theory
§3 Idempotency equation
§4 Solitonic states
§5 Conclusion and discussion
Plan of the talk
![Page 7: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/7.jpg)
7
§2 OSp invariant string field theory
light-cone gauge SFT
O(25,1) symmetry
OSp invariant SFT Grassmann
OSp(27,1|2) symmetrySiegel, Uehara, Neveu, West,Zwiebach, Kugo, ….
![Page 8: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/8.jpg)
8
OSp theory covariant string theory with extra time and length
BRS symmetry
the string field Hamiltonian is BRS exact
![Page 9: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/9.jpg)
9
・string length joining-splitting interaction extra time variable etc.
similar to noncriticalSFT
Can we construct solitonic operators?
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
OSp theory Parisi-Sourlas, stochastic quantizationMarinari-Parisi for c=0
different from the usual formulation, but
![Page 10: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/10.jpg)
10
§3 Idempotency equation
idempotency equation
Kishimoto, Matsuo, Watanabe
regularization
we need to consider boundary states
![Page 11: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/11.jpg)
11
Boundary states in OSp theory
BRS invariant regularization
normalized state:
the boundary state for a flat Dp-brane
![Page 12: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/12.jpg)
12
orthogonal to light-cone quantization
this part of the theory looks quite similar to SFT for c=0
we may be able to construct solitonic operators
![Page 13: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/13.jpg)
13
§4 Solitonic states
these coefficients are fixed by BRS invariance
BRS invariant state
more generally
BRS invariant
![Page 14: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/14.jpg)
14
amplitudes
S-matrix elements
with D-branes
vacuum amplitude
perturbative calculation
saddle point approximation
![Page 15: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/15.jpg)
15
should be identified with the state with two D-branes or ghost D-branes
disk amplitude
(Okuda, Takayanagi)
Baba, Murakami, N.I. to appear
![Page 16: D-branes and Closed String Field Theoryhep1.c.u-tokyo.ac.jp/workshop/komaba2007/ishibashi.pdf · 2007-02-15 · §1 Introduction D-branes in string field theory. 3 String Field l](https://reader033.vdocument.in/reader033/viewer/2022050305/5f6e2516c7afed3ca73ca796/html5/thumbnails/16.jpg)
16
§5 Conclusion and discussion
♦similar construction for superstrings
♦other amplitudes
♦1 D-brane
♦ghost D-branes ~ annihilation operators for D-branes?
?
2nd quantization Yoneya-san’s talk
-brane BRS invariant state in OSp invariant SFT