Abstract
We construct several BV master actions for open superstring field theory in the large Hilbert space. First, we show that a naive use of the conventional BV approach breaks down at the third order of the antifield number expansion, although it enables us to define a simple “string antibracket” taking the Darboux form as spacetime antibrackets. This fact implies that in the large Hilbert space, “string fields-antifields” should be reassembled to obtain master actions in a simple manner. We determine the assembly of the string anti-fields on the basis of Berkovits’ constrained BV approach, and give solutions to the master equation defined by Dirac antibrackets on the constrained string field-antifield space. It is expected that partial gauge-fixing enables us to relate superstring field theories based on the large and small Hilbert spaces directly: reassembling string fields-antifields is rather natural from this point of view. Finally, inspired by these results, we revisit the conventional BV approach and construct a BV master action based on the minimal set of string fields-antifields.
Highlights
A successful formulation of open superstring field theory was first proposed by Berkovits [14], which is characterized by a string field living in the large Hilbert space [15] and a Wess-Zumino-Witten-like (WZW-like) action having the large gauge invariance
In the most of this paper, we focus on the Neveu-Schwarz (NS) sector of open superstring field theory, the large A∞ theory
There is no criteria or rule for how to assemble string antifields unlike string ghost fields in the BV formalism: it just suggests that how or what kind of spacetime ghost fields must be introduced from the gauge invariance, and one can introduce their spacetime antifields such that the antibracket takes the Darboux form
Summary
We clarify how to apply the BV formalism to superstring field theory in the large Hilbert space by using the large A∞ theory — the simplest example of the WZW-like formulation. Let Φ be a Neveu-Schwarz (NS) open superstring field living in the large Hilbert space, which carries world-sheet ghost number 0 and picture number 0. We write ηA, ηB bpz for the BPZ inner product of ηA and ηB in the small Hilbert space, which equals to the BPZ inner product A, ηB bpz = −(−)A ηA, B bpz in the large Hilbert space This small A∞ theory is gauge-fixable iff all string fields of gauge parameters and their gauge algebras are restricted to the small Hilbert space: one can construct its BV master action Sb′ v by just relaxing ghost number constraint as Sb′ v ≡ S′[ψ] where ψ carries all spacetime and world-sheet ghost numbers. The BV master action Sbv for the large A∞ action (2.1a) in a similar manner because of its WZW-like large gauge symmetries, S[Φ] is obtained from the trivial embedding of gauge-fixable S′[Ψ], which we explain
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