The Noncommutative Bion Core

TL;DR

The paper shows that $N$ coincident D-strings with a nonabelian worldvolume action admit noncommutative funnel solutions in which the D-strings expand into a D3-brane, a configuration dual to the abelian D3-brane spike. In the large $N$ limit, energy, RR couplings, and the funnel geometry agree with the D3-brane spike picture, and D-string fluctuations match as well; at finite $N$ the noncommutative structure imposes a maximum angular momentum $ll_{ m max}=N-1$, limiting propagating modes. The work extends to double funnels, $(p,q)$-strings, and embeddings in D3-brane backgrounds, providing a coherent dual framework for D-strings ending on D3-branes. It also analyzes the regime of validity, higher-derivative corrections, and the role of boundary conditions and representations in shaping the noncommutative geometry of the core. These results highlight the complementary insights provided by nonabelian D-string dynamics alongside the conventional D3-brane spike description.

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.