D-Branes, Tachyons, and String Field Theory

TL;DR

The notes survey tachyon condensation in bosonic OSFT, linking open-string tachyon physics to brane decay and nonperturbative backgrounds. They present both CFT and oscillator formulations, derive the tachyon potential at low levels, and provide substantial evidence for Sen's conjectures, including the brane tension cancellation and D-brane solitons. The work also introduces vacuum string field theory (VSFT) and projector-based brane reconstructions, discusses decoupling of open strings in the true vacuum, and explores the prospects for a background-independent, nonperturbative formulation of string theory, while acknowledging technical and conceptual hurdles. Overall, the framework suggests that OSFT captures essential nonperturbative physics of open strings and branes, potentially illuminating the emergence of backgrounds and the role of closed strings, even as key questions about analytic solutions and closed-string inclusion remain open. An explicit testable hallmark is the relation $T_{25}=1/(2\pi^2 g^2)$ and the near-complete cancellation of D-brane energy in the tachyon vacuum, as evidenced by level-truncation analyses and Padé extrapolations toward $E_ ext{vac}=-T_{25}$.

Abstract

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.

Figures (11)

• Figure 1: T-duality takes a diagonal D1-brane on a two-torus (a) to a D2-brane on the dual torus with constant magnetic flux encoding an embedded D0-brane (b).
• Figure 2: A pair of crossed D1-branes, T-dual to a pair of D2-branes with uniformly embedded D0- and anti-D0-branes.
• Figure 3: The brane-antibrane instability of a D0-D$\bar{0}$ system embedded in two D2-branes, as seen in the T-dual D1-brane picture.
• Figure 4: Representation of the cubic vertex as the gluing of 3 half--disks.
• Figure 5: Representation of the cubic vertex as a 3--punctured unit disk.