Fixing an ambiguity in two dimensional string theory using string field theory

In a recent paper, Balthazar, Rodriguez and Yin found some remarkable agreement between the results of c = 1 matrix model and D-instanton corrections in two dimensional string theory. Their analysis left undetermined two constants in the string theory computation which had to be fixed by comparing the results with the matrix model results. One of these constants is affected by possible renormalization of the D-instanton action that needs to be computed separately. In this paper we fix the other constant by reformulating the world-sheet analysis in the language of string field theory.