The polarization of F1 strings into D2 branes: "Aut Caesar aut nihil"

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 F1 -> D2 polarizations (Caesar) for some fractional strengths of the perturbation, and of no polarization whatsoever (nihil) 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 is does not confirm or disprove the symmetrized trace prescription.