The Noncommutative Bion Core

TL;DR

This paper explores noncommutative solutions describing D-strings expanding into D3-branes, establishing duality with abelian monopole solutions and analyzing their physical properties, especially in the large N limit.

Contribution

It introduces noncommutative D-string solutions that accurately describe monopole cores and confirms their agreement with abelian descriptions in the large N limit.

Findings

Good agreement between noncommutative and abelian descriptions at large N

Constraints on modes traveling along D-strings at finite N

Noncommutative solutions effectively model monopole cores

Abstract

We examine noncommutative solutions of the nonabelian theory on the world-volume of N coincident D-strings. These solutions can be interpreted in terms of noncommutative geometry as funnels describing the nonabelian D-string expanding out into an orthogonal D3-brane. These configurations are `dual' to the bion solutions in the abelian world-volume theory of the D3-brane. In the latter, a charge N magnetic monopole describes N D-strings attached to the D3-brane with a spike deformation of the world-volume. The noncommutative D-string solutions give a reliable account of physics at the core of the monopole, where the bion description is expected to breakdown. In the large N limit, we find good agreement between the two points of view, including the energy, couplings to background fields, and the shape of the funnel. We also study fluctuations traveling along the D-string, again obtaining agreement in the large N limit. At finite N, our results give a limit on the number of modes that can travel to infinity along the N D-strings attached to the D3-brane.