# Deformation of the Cubic Open String Field Theory

## TL;DR

This paper introduces a consistent deformation of cubic open string field theory that maps non-planar diagrams to planar ones, reproduces Yang-Mills theory in the zero-slope limit, and enables calculation of multi-string scattering amplitudes.

## Contribution

It presents a novel deformation of cubic open string field theory that correctly relates string and Yang-Mills couplings and facilitates multi-string amplitude computations.

## Key findings

- Deformation maps non-planar diagrams to planar diagrams.
- Reproduces non-Abelian Yang-Mills action in the zero-slope limit.
- Enables calculation of scattering amplitudes with multiple open strings.

## Abstract

We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang-Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang-Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.