Polarization ofF1strings into D2 branes

We give matrix and supergravity descriptions of type IIA F strings polarizing into cylindrical D2 branes. When a RR four-form field strength $F_4$ is turned on in a supersymmetric fashion (with 4 supercharges), a complete analysis of the solutions reveals the existence of a moduli space of $F\overrightarrow{1}\mathrm{D}2$ polarizations for some fractional strengths of the perturbation, and of no polarization whatsoever for all other strengths of the perturbation. This is a very intriguing phenomenon, whose physical implications we can only speculate about. In the matrix description of the polarization we use the non-Abelian Born-Infeld action in an extreme regime, where the commutators of the fields are much larger than 1. The validity of the results we obtain provides a direct confirmation of this action, although it does not confirm or disprove the symmetrized trace prescription.