Abstract
In a previous paper it was shown that the recently constructed action for open superstring field theory based on A ∞ algebras can be re-written in Wess-Zumino-Witten-like form, thus establishing its relation to Berkovits’ open superstring field theory. In this paper we explain the relation between these two theories from a different perspective which emphasizes the small Hilbert space, and in particular the relation between the A ∞ structures on both sides.
Highlights
The basic idea behind the construction of the A∞ superstring field theory is that string interactions can be generated by performing a kind of “field redefinition” from a free theory
Turning this into a cohomomorphism, we conclude that the generic NS open superstring field theory has an A∞ structure at least at the level of the equations of motion, and that there is a corresponding set of products, gauge products, and bare products which satisfy the analogue of (4.73)-(4.75)
In this paper we have shown that the A∞ superstring field theory is related to a free theory through the improper field redefinition given in (3.44)
Summary
We describe the coalgebra representation of A∞ algebras. Some of this is reviewed in recent papers [1, 4, 7], but we will need some further elaborations, especially about cohomomorphisms and their relation to field redefinitions. We will mostly use degree as our grading, and multi-string products will be defined with the corresponding sign. The degree of a linear map is defined as the degree of its output minus the sum of the degrees of its inputs, and the sign on the right hand side can be interpreted as arising from (anti)commuting cn,l past the first m states. With this we can rexpress the derivation property of Q and associativity of the star product. Acting the first equation on A ⊗ B and the second equation on A ⊗ B ⊗ C, and using (2.3), we recover the expected expressions (2.7) and (2.8)
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