Projection Operators and D-branes in Purely Cubic Open String Field Theory

TL;DR

This paper explores a matrix formulation of purely cubic open string field theory, showing how D-branes emerge as classical solutions and analyzing the resulting open string dynamics around these solutions.

Contribution

It introduces a matrix approach to purely cubic open string field theory and demonstrates how D-branes can be represented as classical solutions using identity projectors.

Findings

D-branes appear as classical solutions in the matrix theory.

The expansion around these solutions yields correct open string kinetic terms.

Subtleties exist in handling unwanted degrees of freedom.

Abstract

We study a matrix version of the purely cubic open string field theory as describing the expansion around the closed string vacuum. Any D-branes in the given closed string background can appear as classical solutions by using the identity projectors. Expansion around this solution gives the correct kinetic term for the open strings on the created D-branes while there are some subtleties in the unwanted degree of freedom.