Soluzione effettiva di vortice nel sistema Brana/Anti-brana.

Nowadays we're interested in exact classical solutions of the string theory which can describe different consistent backgrounds. The analysis of the low energy effective action is helpful to approximate classical solutions that we are not yet able to construct in a full microscopic approach. In this thesis, we estimate the effective action by using the string field theory approach in Berkovits' superstring and we take as an example the case of the $D\bar D$-branes system. Once the effective potential is evaluated we recognize the Abelian-Higgs potential. After examining the corresponding classical Nielsen-Olesen vortex solutions, we are able to find analogous solutions for the superstring effective action that we compute from OSFT. Thanks to these effective solutions we can approximate the full microscopic solution thanks to the homotopy transfer which maps solutions of the effective theory to solutions of the full microscopic theory.