Tachyon Condensation: Calculations in String Field Theory

TL;DR

This work investigates tachyon condensation in open string field theories, applying Witten's cubic SFT to the bosonic string and Berkovits' WZW-like SFT to the superstring. It develops and employs level-truncation methods to compute tachyon potentials at progressively higher levels, showing convergence toward Sen's conjectures with approximately 68–94% agreement across levels in different setups, and notably achieving about 94.4% at level (4,8) in Berkovits' theory via conservation-law techniques. The introduction of conservation laws markedly improves computational efficiency, enabling higher-level results that strengthen the case for Berkovits' superstring field theory as a viable off-shell description of open superstrings. A complementary toy model provides analytic insight into the algebraic structure and vacuum solutions, illustrating how truncation and derivations can illuminate the path toward the true vacuum and the possible emergence of closed strings. Overall, the thesis substantiates the utility of string field theory in addressing nonperturbative questions about D-brane decay, tachyon dynamics, and the open/closed string relationship, while highlighting the efficacy of Berkovits' framework for open superstrings and the value of simplified models for conceptual progress.

Abstract

In this Ph.D. thesis, we study tachyon condensation in string field theories. In chapter 2, we review Witten's bosonic string field theory and calculate the tachyon potential. In chapter 3, we calculate the tachyon potential in Berkovits' superstring field theory. In chapter 4, we look for exact solutions in a toy model. Unpublished result: we use conservation laws to calculate the level (4,8) approximation of the tachyon potential in Berkovits' superstring field theory. We verify Sen's conjecture up to 94.4%.

Figures (21)

• Figure 1: (1) A closed string approaches a $D$-brane. (2) The closed string interacts with the $D$-brane by way of the (virtual) open strings attached to it. (3) After the collision, the closed string moves away.
• Figure 2: The tachyon potential in the open bosonic string theory. In point $A$, the string field $\Psi$ is zero. At this point, the unstable $D25$-brane is still present. Point $B$ is the closed string vacuum. According to the conjecture of Sen, the $D25$-brane decays to this vacuum. Therefore, the difference in potential energy between these two extrema equals the mass of the $D25$-brane.
• Figure 3: The tachyon potential on the unstable $D9$-brane.
• Figure 4: (a) An open string having its endpoints on a non-BPS $D$-brane before tachyon condensation. The endpoints of the open string are charged under a gauge field. (b) This configuration after tachyon condensation. The open strings together with the flux tube form a closed string.
• Figure 5: Representation of the cubic vertex as the gluing of three half-disks. The arrows on the boundaries specify the way these boundaries should be glued.

Theorems & Definitions (12)

• Definition 2.1
• Definition 2.2
• proof
• Definition 2.3
• proof
• proof
• proof
• Definition 1.1
• Definition 1.2
• proof