# Light-cone reduction of Witten's open string field theory

## TL;DR

This paper establishes a precise connection between light-cone and covariant string field theories using homological perturbation, leading to a new light-cone string field theory derived from Witten's open string field theory.

## Contribution

It introduces an exact reduction method for gauge degrees of freedom in covariant string theory, resulting in a novel light-cone string field theory.

## Key findings

- Derived a refined no-ghost theorem for covariant strings.
- Provided an exact gauge-fixing procedure incorporating interactions.
- Constructed a new light-cone string field theory from Witten's framework.

## Abstract

We elucidate some exact relations between light-cone and covariant string field theories on the basis of the homological perturbation lemma for $A_{\infty }$. The covariant string field splits into the light-cone string field and trivial excitations of BRST quartets: The latter generates the gauge symmetry and covariance. We first show that the reduction of gauge degrees can be performed by applying the lemma, which gives a refined version of the no-ghost theorem of covariant strings. Then, we demonstrate that after the reduction, gauge-fixed theory can be regarded as a kind of effective field theory and it provides an exact gauge-fixing procedure taking into account interactions. As a result, a novel light-cone string field theory is obtained from Witten's open string field theory.