Witten's Cubic Open String Field Theory on multiple $Dp$-branes

TL;DR

This paper develops a detailed Fock space representation of Witten's cubic open string field theory on multiple Dp-branes, connecting string interactions to low-energy non-Abelian gauge theories.

Contribution

It provides a Fock space formulation for multi-brane string interactions and demonstrates the reduction to non-Abelian gauge theory cubic terms.

Findings

Derived explicit vertex operators for multiple Dp-branes

Showed the low-energy limit reproduces non-Abelian gauge interactions

Established the string field theory as a tool for quantum Dp-brane dynamics

Abstract

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.