Azione effettiva in Teoria di Campo di Stringa e Background Independence

In this thesis we work in the subject of open bosonic String field theory, in particular we focus on the Erler-Maccaferri solution of the background independence conjecture. The conjecture requires to prove the following statement: consider the open string field theory of a chosen starting D-brane. The classical equations of motion of this theory have solutions describing every possible target D-brane systems which share the same closed string background. Moreover, the field theory of fluctuations around a solution can be related to the string field theory of the corresponding D-brane by field redefinition. Great progress towards a rigorous prove of this statement have been recently made, in particular the newly constructed Erler-Maccaferri string states provide an actual description of every target D-brane system as a classical solution of the open string field theory defined on a staring D-brane. In their original paper they also suggest a suitable field redefinition that unfortunately does not represent an isomorphism between the Hilbert spaces of the starting D-brane and the target D-brane, and it may alter the description of the perturbation theory around the latter from the starting background point of view. In this thesis we managed to prove, working with algebraic methods used to evaluate effective actions, that, at least at tree level, the lack of invertibility of this particular map does not bring any effect on the physics of the target system, and it can be actually considered as the good field redefinition required to prove the original conjecture