Noncommutative bion core - art. no. 106009

We examine noncommutative solutions of the non-Abelian theory on the world- volume of N coincident D-strings. These solutions can be interpreted in ter ms of noncommutative geometry as funnels describing the non-Abelian D-strin g 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 noncommu tative D-string solutions give a reliable account of physics at the core of the monopole, where the bion description is expected to break down. In the large N limit, we find good agreement between the two points of view, incl uding the energy, couplings to background fields, and the shape of the funn el. We also study fluctuations traveling along the D-string, again obtainin g 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 attac hed to the D3-brane.