A Review on Tachyon Condensation in Open String Field Theories

TL;DR

Open string field theory is used to study tachyon condensation on unstable D-branes in both bosonic and superstring theories, testing brane annihilation to a closed string vacuum and the formation of lower-dimensional branes as tachyonic lumps. The review surveys Witten's cubic formalism, level-truncation results, and background independent OSFT, showing that the universal tachyon potential approaches the expected brane tension cancellation with increasing level, supporting the Descent conjecture. It also covers lump solutions that realize lower-dimensional D-branes, analyzes the fate of world-volume gauge fields at the nonperturbative vacuum, and discusses off-shell formulations in various superstring field theories (cubic, modified, and Berkovits' WZW-like). While the results consistently indicate brane decay to a closed string vacuum and reveal rich structure in the gauge and BRST sectors, several nonperturbative and off-shell issues—such as gauge-field dynamics and equivalence of different SFT formulations—remain open challenges with important implications for string phenomenology. Overall, the work provides a coherent, multilayered framework linking tachyon dynamics, brane descent, and lump construction across bosonic and superstring theories.

Abstract

We review the recent studies of tachyon condensation in string field theory. After introducing the open string field theory both for bosonic string and for superstring, we use them to examine the conjecture that the unstable configurations of the D-brane will decay into the `closed string vacuum' through the tachyon condensation. And we describe the attemps to construct a lower dimensional bosonic D-brane as an unstable lump solution of the string field equation. We obtain exact results from another formulation, background independent open string field theory. We also discuss some other topics which are related to tachyon condensation in string theory, such as the construction of a D-brane as a noncommutative soliton and some field theory models. This paper is based on my master's thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2001.

Figures (30)

• Figure 1: (a) Gluing of two strings $S,T$. (b) Gluing of three strings $S,T,U$ makes the associativity clear. (c) Integration operation. (d) Multiplication followed by an integration, $\int (a*b)$.
• Figure 2: 5-string vertex.
• Figure 3: Three strings which will interact.
• Figure 4: From an upper half disk to one third of a unit disk.
• Figure 5: 3-string vertex.