Open string fields and D-branes

These lecture notes review some modern developments in open string field theory. We begin with a discussion of the physical motivations and general framework of open SFT. We then briefly introduce and contrast the two basic formalisms, Boundary SFT and cubic SFT, and summarize the main results about tachyon condensation obtained with both approaches. Next, we review the Vacuum SFT conjecture, according to which D-brane solutions correspond to string fields that are projectors of Witten's *-algebra. We describe the Boundary CFT technique to compute *-products and construct projector solutions. We argue that VSFT accounts precisely for the expected moduli space of D-branes.