# Covariant Open String Field Theory on Multiple $Dp$-Branes

## TL;DR

This paper develops a covariant open string field theory framework for multiple Dp-branes, deriving effective actions that connect to matrix models like BFSS and IKKT, and discusses potential for non-perturbative quantum field theory insights.

## Contribution

It constructs the Fock space representations of string vertices on multiple Dp-branes and links the effective action to well-known matrix models in the zero-slope limit.

## Key findings

- Effective action reduces to BFSS matrix model for D0-branes.
- Relation established between string field theory on D-instantons and IKKT matrix model.
- Framework allows systematic evaluation of non-zero-slope corrections.

## Abstract

We study covariant open bosonic string field theories on multiple $Dp$-branes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple $Dp$-branes, we obtain the field theoretical effective action in the zero-slope limit. On the multiple $D0$-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between the open string field theory on multiple $D$-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple $Dp$-branes would be useful to study the non-perturbative properties of quantum field theories in $(p+1)$-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using the covariant string field theory.