Abstract
Abstract We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach’s construction for the bosonic string. The construction uses the small Hilbert space. Elementary vertices of the non-polynomial action are described with the help of a properly formulated minimal area problem. They give rise to an infinite tower of superstring field products defining a $ \mathcal{N} $ = 1 generalization of a loop homotopy Lie algebra, the genus zero part generalizing a homotopy Lie algebra. Finally, we give an operadic interpretation of the construction.
Highlights
Moduli space, such that the moduli space decomposes uniquely into vertices and graphs, and do not apriori require a background
In an almost unnoticed work [12], the geometric approach developed in bosonic closed string field theory, as described in the previous paragraph, has been generalized to the context of superstring field theory
The purpose of this paper is to describe the construction of type II superstring field theory in the geometric approach
Summary
The basic requirement of string field theory is, that its vertices reproduce the perturbative string amplitudes via Feynman rules. As in the NS sector, the sewing with I(±,−) in the non-separating case generates a handle with ± spin structure along the B-cycle. The family of local coordinate systems associated to a coordinate curve in the NS sector is parametrized by an angle θ ∈ [0, 2π] and the corresponding sewing operation is given by φθ = INS ◦ φli0θ = ΠGSO− ◦ I(+,+) ◦ φli0θ ,. That in the R sector the family of local coordinate systems associated to a coordinate curve is parametrized by an angle θ ∈ [0, 2π] and an odd parameter τ ∈ C0|1, and the corresponding sewing operation reads φ±θ,τ = IR± ◦ φgiθ0,τ = ΠGSO± ◦ I(+,−) ◦ φgiθ0,τ. We do not describe this operation here, but definitely it can be defined to the bosonic case by disjoint union [11, 21]
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