Gauge Invariance and Tachyon Condensation in Open String Field Theory

TL;DR

This work analyzes gauge invariance in Witten's cubic open string field theory through level truncation, clarifying that FS gauge breaks down at a calculable boundary and that apparent branch points in the tachyon potential are gauge artifacts. By comparing FS-gauge results with gauge-free and alternative-gauge approaches, the authors show that tachyon condensation is consistent with background-independent string field theory, where the tachyon potential is unbounded below, and that the stable vacuum can be approached reliably within FS gauge, aided by additional gauge-invariance constraints. The paper provides a concrete framework for understanding gauge artifacts via the determinant condition $\det M_{qb}=0$, and discusses how to explore vacua without fixing FS gauge or in other gauges, though no significantly superior alternative gauge is found. Overall, the results strengthen the interpretation of tachyon condensation within open SFT and highlight the role of gauge-viability boundaries in level-truncated analyses.

Abstract

The gauge invariance of open string field theory is considered from the point of view of level truncation, and applications to the tachyon condensation problem are discussed. We show that the region of validity of Feynman-Siegel gauge can be accurately determined using the level truncation method. We then show that singularities previously found in the tachyon effective potential are gauge artifacts arising from the boundary of the region of validity of Feynman-Siegel gauge. The problem of finding the stable vacuum and tachyon potential without fixing Feynman-Siegel gauge is addressed.

Figures (3)

• Figure 1: Successive approximations to boundary of region of Feynman-Siegel gauge validity near origin, in units of $1/3 g\kappa$
• Figure 2: Sign[$\det M_{qb}$] at levels (4, 12), (6, 18), and (8, 16)
• Figure 3: $\det M_{qb}$ in level (4, 8) truncation along tachyon potential.