Mapping between Witten and Lightcone String Field Theories

TL;DR

This paper introduces a transformation linking Witten's open bosonic string field theory to lightcone string field theory, revealing a direct correspondence through vertex deformation and oscillator integration.

Contribution

It presents a novel method to map off-shell variables between two string field theories, showing their equivalence via vertex deformation and oscillator integration.

Findings

The transformation preserves cubic and quartic interactions.

Integrating out ghost and lightcone oscillators does not alter the interactions.

The resulting theory matches Kaku and Kikkawa's lightcone string field theory.

Abstract

We propose a transformation between the off-shell field variables of Witten's open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam's interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa's lightcone string field theory.