Dynamics of strings in noncommutative gauge theory

We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N = 4U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1-strings that pierce a D3-brane at various points, in the presence of a background B-field in the Seiberg-Witten α′ → 0 limit. We call this solution the N-fluxon. For N = 1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1 strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point - corresponding to fundamental strings stretched between the D1-string and the D3-brane. We discuss the fluctuations about the N-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zero modes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution.