# Supersymmetric DBI Equations in Diverse Dimensions from BRS Invariance of Pure Spinor Superstring

## TL;DR

This paper derives supersymmetric Dirac-Born-Infeld (DBI) equations for D-branes from BRS invariance in pure spinor superstring theory, establishing a connection between string invariance and brane dynamics.

## Contribution

It demonstrates that BRS invariance of the pure spinor superstring yields supersymmetric DBI equations for background superfields on Dp-branes, extending previous results to diverse dimensions.

## Key findings

- BRS invariance imposes boundary conditions on spacetime spinors.
- Supersymmetric DBI equations are derived from BRS invariance.
- Results are consistent with known D9-brane equations.

## Abstract

We examine the BRS invariance of the open pure spinor superstring in the presence of background superfields on a Dp-brane. It is shown that the BRS invariance leads not only to boundary conditions on the spacetime spinors, but also to supersymmetric DBI equations of motion for the background superfields on the Dp-brane. These DBI equations are consistent with the supersymmetric DBI equations for a D9-brane.