Open string field theory in a non-trivial background field: (II). Feynman rules and four-point amplitudes

Abstract

In a previous paper we wrote down the gauge-invariant action for open string field theory in an arbitrary background field describing a two-dimensional conformal field theory on the upper half-plane. In this paper we discuss the gauge fixing and the calculation of tree-level four-point amplitude in this string field theory, and show that the result agrees with the answer expected from the appropriate four-point correlation function in conformal field theory.