Closed string deformations in open string field theory II: superstring

TL;DR

This paper develops a method to compute effective open-closed superstring couplings by integrating out massive fields in superstring field theory, providing all-order results and new gauge-invariant observables.

Contribution

It introduces a novel large Hilbert space perturbation theory and a new $A_$ observable for gauge-invariant open-closed couplings in superstring field theory.

Findings

Explicit first-order vacuum shift solutions and obstructions.

All-order effective open-closed couplings in the small Hilbert space.

A new gauge-invariant observable in $A_$ theory.

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.