Closed string deformations in open string field theory II: superstring

Abstract

This is the second paper of a series of three. We construct effective open-closed superstring couplings by classically integrating out massive fields from open superstring field theories coupled to an elementary gauge invariant tadpole proportional to an on-shell closed string state in both large and small Hilbert spaces, in the NS sector. This source term is well known in the WZW formulation and by explicitly performing a novel large Hilbert space perturbation theory we are able to characterize the first orders of the vacuum shift solution, its obstructions and the non-trivial open-closed effective couplings in closed form. With the aim of getting all order results, we also construct a new observable in the $A_{\infty }$ theory in the small Hilbert space which correctly provides a gauge invariant coupling to physical closed strings and which descends from the WZW open-closed coupling upon partial gauge fixing and field redefinition. Armed with this new $A_{\infty }$ observable we use tensor co-algebra techniques to efficiently package the whole perturbation theory necessary for computing the effective action and we give all order results for the open-closed effective couplings in the small Hilbert space.

arXiv comment35 pages, no figures. V2: 39 pages, an explicit example of superstring mass deformation added. JHEP version

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Cited by in corpus (6)

• The classical cosmological constant of open-closed string field theory
• String Field Theory
• Closed string deformations in open string field theory I: bosonic string
• Closed string deformations in open string field theory III: $\mathcal{N}=2$ worldsheet localization
• Symplectic structure in open string field theory III: Electric field
• Algebraic Structures In Closed Superstring Field Theory, Homotopy Transfer And Effective Actions