Boundary state of multiple D0-branes and closed string coupling

TL;DR

This paper constructs a boundary state for multiple D0-branes with spacetime-dependent scalar fields, demonstrating its BRST invariance, consistency with supergravity, and agreement with known D-brane configurations, up to order .

Contribution

It introduces a non-Abelian boundary state for multiple D0-branes with scalar fields, ensuring BRST invariance and matching known physical results, advancing boundary state formulations.

Findings

Boundary state is BRST invariant when scalar fields satisfy equations of motion.

Reproduces supergravity current distributions from disk amplitudes.

Matches known configurations like boosted D0-branes and noncommutative D2-branes.

Abstract

In this paper we study a boundary state of multiple D0-branes with spacetime dependent scalar fields in the \alpha' expansion. We calculate a formulas for non-Abelian boundary state defined by using a Wilson loop factor and path ordering. The boundary state contains divergences which vanish when the scalar fields on D0-branes satisfy the equation of motion. Hence the boundary state is well-defined if the configuration of D0-branes in on-shell. We can show the constructed boundary state is BRST invariant. From the constructed boundary state we extract couplings of the scalar fields to closed string fields. Our results reproduce the correct formulas for supergravity current distribution obtained from the disk amplitudes, Matrix theory potential, non-Abelian DBI action. Our calculations are performed up to order {\alpha'}^2 both in the bosonic string and the IIA superstring theory. Furthermore we confirm that our boundary state is identical to the correct one in the case of a single boosted D0-brane and a noncommutative D2-brane. These results support the correctness of the formulas for non-Abelian boundary states.