Open string states and D-brane tension from vacuum string field theory

TL;DR

This work presents a concrete description of open string fields on a D25-brane within vacuum string field theory, identifying open-string states with boundary insertions on the matter sliver and showing that the physical-state conditions yield the correct tachyon mass and full open-string spectrum. By reformulating the VSFT action in terms of these open-string fields, the author computes the tachyon kinetic term and the on-shell three-tachyon coupling, demonstrating that the D25-brane tension $T_{25}$ is correctly expressed as $T_{25} = \frac{1}{2 \pi^2 \alpha'^3 g_T^2}$, with the classical energy matching $T_{25}$. The results connect VSFT to boundary string field theory and BSFT-like frameworks, address large-$n$ renormalization issues, and discuss the role of the ghost sector, offering a coherent picture that reproduces key perturbative open-string data within VSFT. These findings provide a consistent dictionary between VSFT solutions and conventional open-string physics, with implications for non-Abelian extensions and deeper links to BSFT and Witten’s SFT.

Abstract

We propose a description of open string fields on a D25-brane in vacuum string field theory. We show that the tachyon mass is correctly reproduced from our proposal and further argue that the mass spectrum of all other open string states is correctly obtained as well. We identify the string coupling constant from the three-tachyon coupling and show that the tension of a D25-brane is correctly expressed in terms of the coupling constant, which resolves the controversy in the literature. We also discuss a reformulation of our description which is rather similar to boundary string field theory.

Figures (1)

• Figure 1: The tachyon potential $V(T)$. The horizontal axis is $aT$ and the vertical axis is $V(T)/T_{25}$. The sliver state corresponds to $T=0$ and the tachyon vacuum corresponds to $T=\infty$.