Witten’s cubic open string field theory on multiple Dp-branes

We study Witten’s cubic open string field theory on multiple Dp -branes. On multiple Dp -branes the string fields carry U ( N ) group indices. Mapping the string world-sheet onto the upper half complex plane and evaluating the Polyakov string path integral of Witten’s cubic open string, we obtain a Fock space representation of one, two and three-string vertex operators. In the low energy region, the system is described by massless gauge fields and massless scalar fields, carrying U ( N ) group indices. The two-string vertex induces mass terms for the gauge fields and the scalar fields. The cubic interaction reduces correctly to the cubic term of the non-Abelian gauge fields, cubic interaction terms of the gauge fields, and the scalar fields on ( p + 1 ) dimensional space. Thus, Witten’s string field theory may be a useful tool to study the quantum dynamics of open strings on multiple Dp -branes.