D - Branes , Tachyons , and String Field Theory

In these notes we provide a pedagogical introduction to the subject of tachyon condensation in Witten's cubic bosonic open string field theory. We use both the low-energy Yang-Mills description and the language of string field theory to explain the problem of tachyon condensation on unstable D-branes. We give a self-contained introduction to open string field theory using both conformal field theory and overlap integrals. Our main subjects are the Sen conjectures on tachyon condensation in open string field theory and the evidence that supports these conjectures. We conclude with a discussion of vacuum string field theory and projectors of the star-algebra of open string fields. We comment on the possible role of string field theory in the construction of a nonperturbative formulation of string theory that captures all possible string backgrounds.