Noncommutative Geometry of Multicore Bions

TL;DR

This paper presents new BPS solutions in nonabelian D-brane theory, illustrating topology change in noncommutative geometry by describing how D1-brane bundles form a D3-brane with two spikes, matching abelian results at finite N.

Contribution

It introduces explicit nonabelian solutions for D1-branes expanding into a D3-brane, demonstrating topology change and finite N agreement with abelian models.

Findings

New BPS solutions for parallel D1-branes forming a D3-brane

Finite N agreement with abelian Born-Infeld shape

Explicit realization of topology change in noncommutative geometry

Abstract

We find new BPS solutions to the nonabelian theory on a world-volume of parallel D1-branes. Our solutions describe two parallel, separated bundles of N D1-branes expanding out to form a single orthogonal D3-brane. This configuration corresponds to two charge N magnetic monopoles in the world-volume of a single D3-brane, deforming the D3-brane into two parallel spikes. We obtain the emergent surface corresponding to our nonabelian D1-brane configuration and demonstrate, at finite N, a surprisingly accurate agreement with the shape of the D3-brane world-volume as obtained from the abelian Born-Infeld action. Our solution provides an explicit realization of topology change in noncommutative geometry at finite N.