Open string field theory, unstable D-branes and open-closed duality

In this thesis we explore different aspects of unstable D-brane dynamics and open-closed dualities. The first chapters focus on the properties of the so-called “tachyon vacuum” for unstable D-branes, that is conjectured to describe the complete decay of the D-brane, using the tool of Open String Field Theory. The first chapter discusses a numerical analysis of this vacuum state, the second discusses and motivates a conjecture on the structure of String Field Theory around the vacuum state and the third presents in more detail some important analytic tools that appeared in chapter two.; We shift the focus in chapter four to a time-dependent version of the tachyon decay process and to the duality between some configurations of D-branes in the imaginary time direction and some purely closed wave-like backgrounds. Similar ideas have an application in noncritical string theories in the context of the identification of D-branes as the basic degrees of freedom of the theory. In chapter five we discuss one particular aspect of this identification in the context of the (2, 1) noncritical string (2d topological gravity): we reduce Open String Field Theory on the stable D-branes of the (2, 1) model to the Kontsevich matrix integral, that is known to encode the whole closed string theory for the (2, 1) model.