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The Berkovits formulation of open superstring field theory is based on thelarge Hilbert space of the superconformal ghost sector. We discuss its relationto the Witten formulation based on the small Hilbert space. We introduce aone-parameter family of conditions for partial gauge fixing of the Berkovitsformulation such that the cubic interaction of the theory under the partialgauge fixing reduces to that of the Witten formulation in a singular limit. Thelocal picture-changing operator at the open-string midpoint in the Wittenformulation is regularized in our approach, and the divergence in on-shellfour-point amplitudes coming from collision of picture-changing operators isresolved. The quartic interaction inherited from the Berkovits formulationplays a role of adjusting different behaviors of the picture-changing operatorsin the $s$ channel and in the $t$ channel of Feynman diagrams with two cubicvertices, and correct amplitudes in the world-sheet theory are reproduced.While gauge invariance at the second order in the coupling constant is obscuredin the Witten formulation by collision of picture-changing operators, it iswell defined in our approach and is recovered by including the quarticinteraction inherited from the Berkovits formulation.

From the Berkovits formulation to the Witten formulation in open superstring field theory