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In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK)

D-branes and Closed String Field Theory. N. Ishibashi (University of Tsukuba). In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK). hep-th/0603152 ( JHEP 0605:029,2006 ) hep-th/0702xxx. Komaba2007 Recent Developments in Strings and Fields

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In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK)

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  1. D-branes and Closed String Field Theory N. Ishibashi (University of Tsukuba) In collaboration with Y. Baba(Tsukuba) and K. Murakami(KEK) hep-th/0603152 (JHEP 0605:029,2006 ) hep-th/0702xxx Komaba2007 Recent Developments in Strings and Fields On the occasion of T.Yoneya’s 60th birthday Feb. 11, 2007

  2. §1Introduction D-branes in string field theory • D-branes can be realized as soliton solutions in open string field theory • D-branes in closed string field theory? A.Sen,………. Okawa’s talk Hashimoto and Hata HIKKO ♦A BRS invariant source term ♦c is arbitrary

  3. l D-branes in SFT for noncritical strings SFT for c=0 Kawai and N.I., Jevicki and Rodrigues String Field String Field Theory〜Collective Field Theory in MM Jevicki and Sakita

  4. joining-splitting interactions loop amplitudes Virasoro constraints FKN, DVV

  5. Fukuma and Yahikozawa Hanada, Hayakawa, Kawai, Kuroki, Matsuo, Tada and N.I. Solitonic operators state with D(-1)-brane ghost D-brane these solitonic operators reproduce amplitudes with ZZ-branes c.f.

  6. ♦Can one construct such solitonic operators in SFT for critical strings? Similar construction is possible for OSp invariant string field theory Plan of the talk §2 OSp invariant string field theory §3 Idempotency equation §4 Solitonic states §5 Conclusion and discussion

  7. §2 OSp invariant string field theory light-cone gauge SFT O(25,1) symmetry OSp invariant SFT=light-cone SFT with Grassmann Siegel, Uehara,Neveu, West, Zwiebach, Kugo, …. OSp(27,1|2) symmetry

  8. OSp theory 〜 covariant string theory with extra time and length BRS symmetry the string field Hamiltonian is BRS exact

  9. 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 quantization Marinari-Parisi for c=0 different from the usual formulation, but ・string length ・joining-splitting interaction ・extra time variable etc. similar to noncritical SFT Can we construct solitonic operators?

  10. ∝ §3 Idempotency equation we need to considerboundary states idempotency equation Kishimoto, Matsuo, Watanabe ・regularization

  11. Boundary states in OSp theory the boundary state for a flat Dp-brane ・BRS invariant regularization ・normalized state:

  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

  13. §4 Solitonic states BRS invariant state these coefficients are fixed by BRS invariance more generally BRS invariant

  14. amplitudes S-matrix elements with D-branes vacuum amplitude perturbative calculation saddle point approximation

  15. should be identified with the state with two D-branes or ghost D-branes (Okuda, Takayanagi) ・disk amplitude Baba, Murakami, N.I. to appear

  16. §5 Conclusion and discussion BRS invariant state in OSp invariant SFT ♦D-brane ♦other amplitudes ♦similar construction for superstrings we need to construct OSp SFT for superstrings first ♦1 D-brane ? ♦ghost D-branes 〜 annihilation operators for D-branes ? 2nd quantization Yoneya-san’s talk

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