Abstract
We show that closed string states in bosonic string field theory are encoded in the cyclic cohomology of cubic open string field theory (OSFT) which, in turn, classifies the deformations of OSFT. This cohomology is then shown to be independent of the open string background. Exact elements correspond to closed string gauge transformations, generic boundary deformations of Witten’s 3-vertex and infinitesimal shifts of the open string background. Finally it is argued that the closed string cohomology and the cyclic cohomology of OSFT are isomorphic to each other.
Similar content being viewed by others
References
B. Zwiebach, Quantum open string theory with manifest closed string factorization, Phys. Lett. B 256 (1991) 22 [SPIRES].
B. Zwiebach, Oriented open-closed string theory revisited, Annals Phys. 267 (1998) 193 [hep-th/9705241] [SPIRES].
M.R. Gaberdiel and B. Zwiebach, Tensor constructions of open string theories I: Foundations, Nucl. Phys. B 505 (1997) 569 [hep-th/9705038] [SPIRES].
M. Penkava and A.S. Schwarz, A(infinity) algebras and the cohomology of moduli spaces, hep-th/9408064 [SPIRES].
A. Kapustin and L. Rozansky, On the relation between open and closed topological strings, Commun. Math. Phys. 252 (2004) 393 [hep-th/0405232] [SPIRES].
B. Zwiebach, Interpolating string field theories, Mod. Phys. Lett. A 7 (1992) 1079 [hep-th/9202015] [SPIRES].
J.A. Shapiro and C.B. Thorn, BRST-invariant transitions between closed and open strings, Phys. Rev. D 36 (1987) 432 [SPIRES].
J.A. Shapiro and C.B. Thorn, Closed string-open string transitions and Witten’s string field theory, Phys. Lett. B 194 (1987) 43 [SPIRES].
D. Gaiotto, L. Rastelli, A. Sen and B. Zwiebach, Ghost structure and closed strings in vacuum string field theory, Adv. Theor. Math. Phys. 6 (2003) 403 [hep-th/0111129] [SPIRES].
H. Hata and B. Zwiebach, Developing the covariant Batalin-Vilkovisky approach to string theory, Ann. Phys. 229 (1994) 177 [hep-th/9301097] [SPIRES].
H. Kajiura, Homotopy algebra morphism and geometry of classical string field theory, Nucl. Phys. B 630 (2002) 361 [hep-th/0112228] [SPIRES].
T. Nakatsu, Classical open-string field theory: A(infinity)-algebra, renormalization group and boundary states, Nucl. Phys. B 642 (2002) 13 [hep-th/0105272] [SPIRES].
C.B. Thorn, String field theory, Phys. Rept. 175 (1989) 1 [SPIRES].
I. Ellwood, J. Shelton and W. Taylor, Tadpoles and closed string backgrounds in open string field theory, JHEP 07 (2003) 059 [hep-th/0304259] [SPIRES].
B. Zwiebach, Closed string field theory: Quantum action and the B-V master equation, Nucl. Phys. B 390 (1993) 33 [hep-th/9206084] [SPIRES].
E. Getzler and D.S. Jones, A ∞ -algebras and the cyclic bar complex, Illinois J. Math. 34 (1990) 256.
K. Fukaya, Application of Floer Homology of Lagrangian Submanifolds to symplectic toplogy, in P. Biran et al. (eds.), Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology, (2006), pg. 231–276.
M. Baumgartl, I. Sachs and S.L. Shatashvili, Factorization conjecture and the open/closed string correspondence, JHEP 05 (2005) 040 [hep-th/0412266] [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1010.4125
Rights and permissions
About this article
Cite this article
Moeller, N., Sachs, I. Closed string cohomology in open string field theory. J. High Energ. Phys. 2011, 22 (2011). https://doi.org/10.1007/JHEP07(2011)022
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2011)022