New representation for string field solves the consistency problem for open superstring field theory

On the classical equivalence of superstring field theories

“…Resolutions of these problems can be achieved by leaving the string fields at ghost number one, while modifying their picture number to zero [6,7,8]. The modified cubic action (in the NS+ sector) reads,…”

Open superstring field theory I: gauge fixing, ghost structure, and propagator

“…Such an approach was studied by Berkovits [30]. We did not discuss at all in this work the so-called modified cubic theory [17,18], but we note that a quantization of this theory has been proposed very recently in [31,32]. 8 The complete open superstring field theory includes both Neveu-Schwarz and Ramond sectors.…”

“…This theory describes the Neveu-Schwarz sector of open superstrings using the 'large' Hilbert space of the superconformal ghost sector in terms of ξ, η, and φ [15]. As opposed to some alternative formulations [16,17,18] dt(e −tΦ ∂ t e tΦ ) (e −tΦ Qe tΦ ), (e −tΦ η 0 e tΦ ) .…”

“…In this case one introduces fields φ αn with n ≥ 1 and antifields φ * αn with n ≥ 0 such that the BV action reads 18) where the dots represent terms at least cubic in ghosts and antifields that are needed for a complete solution of the master equation. Since all string fields for "fields" in open superstring field theory are Grassmann even, the R's are Grassmann odd, and since the inner product with (1.3) needed to form the action couples states of the same Grassmann parity, the string fields for "antifields" are Grassmann odd.…”

“…We have thus shown the relation (4.13). Similarly, one can prove 18) where P ∆ − is the projector to the subspace defined by ∆ − . We can also evaluate {Φ (1) + , Φ (2) − } to obtain…”