Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge

TL;DR

This paper develops a covariant open bosonic string field theory on multiple D-branes that simplifies to non-Abelian Yang-Mills theory in the zero-slope limit, providing a new framework for calculating multi-string scattering amplitudes.

Contribution

It introduces a covariant string field theory with planar diagrams that is equivalent to Witten's cubic theory, enabling easier computation of multi-string interactions.

Findings

The theory reduces to non-Abelian Yang-Mills in the zero-slope limit.

Planar world sheet diagrams are generated, contrasting with Witten's cubic theory.

Explicit calculations of three- and four-string vertices confirm the theory's consistency.

Abstract

We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent to the Witten's cubic string field theory. Having obtained planar diagrams, we may adopt the light-cone string field theory technique to calculate the multi-string scattering amplitudes with an arbitrary number of external strings. We examine in detail the three-string vertex diagram and the effective four-string vertex diagrams generated perturbatively by the three-string vertex at tree level. In the zero-slope limit, the string scattering amplitudes are identified precisely as those of non-Abelian Yang-Mills gauge theory if the external states are chosen to be massless vector particles.