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

TL;DR

This paper explores how F1 strings can polarize into D2 branes under specific RR field strengths, revealing a moduli space of solutions and a phenomenon with intriguing physical implications, validated through matrix and supergravity analyses.

Contribution

It provides a detailed matrix and supergravity analysis of F1 to D2 polarization, uncovering a moduli space and conditions for polarization, thus advancing understanding of brane polarization phenomena.

Findings

Existence of a moduli space of polarization solutions

Polarization occurs only at certain fractional field strengths

Validation of the Non-Abelian Born-Infeld action in a specific regime

Abstract

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.