Open-closed string field theory in a background B field

In this paper, we study open-closed string field theory in a background B field in the so-called alpha = p(+) formulation. The string field theory in the infrared limit gives noncommutative gauge theory in the open string sector. Since this theory includes closed string fields as dynamical variables, we can obtain another string field theory in the same background through the condensation of closed string fields, whose low-energy effective action does not exhibit a noncommutativity of spacetime. Although we have two string field theories in the same background, we show that these theories are equivalent. In fact, we give the unitary transformation from string fields in one of them to string fields in the other.