Some Issues in Non-commutative Tachyon Condensation

TL;DR

The paper tackles degeneracy issues in non-commutative tachyon condensation on D-branes, arguing that the observed multiplicity of tachyonic soliton descriptions is a gauge artifact arising from a singular coordinate system at the tachyon vacuum. It introduces non-singular field redefinitions to variables like $ ilde{T}$ and $ ilde{C}_ u$ (and analogues for transverse scalars) that collapse all descriptions to a single, symmetry-restored configuration, consistent with string field theory which shows no flat directions near the vacuum. It then demonstrates restoration of translation invariance and $U( ext{infty})$ gauge symmetry at $T=T_{min}$, shows soliton descriptions with different background data are gauge-equivalent, and explains the absence of unwanted bifundamental open-string states via vacuum equations of motion. Collectively, these results provide a gauge-invariant, background-independent framework for tachyon condensation, reinforcing the interpretation of tachyon solitons as lower-dimensional D-branes.

Abstract

Techniques of non-commutative field theories have proven to be useful in describing D-branes as tachyonic solitons in open string theory. However, this procedure also leads to unwanted degeneracy of solutions not present in the spectrum of D-branes in string theories. In this paper we explore the possibility that this apparent multiplicity of solutions is due to the wrong choice of variables in describing the solutions, and that with the correct choice of variables the unwanted degeneracy disappears.