Tachyon Condensation on Noncommutative Torus

TL;DR

This paper explores noncommutative solitons on a torus and their role in tachyon condensation, revealing a spectrum consistent with T-duality and an inherent instability causing D-brane decay.

Contribution

It provides an exact description of noncommutative solitons using Powers-Rieffel projections and analyzes their implications for D-brane stability and decay.

Findings

Soliton spectrum aligns with T-duality principles

Instability leads to decay into smaller D-branes

Exact soliton descriptions via mathematical projections

Abstract

We discuss noncommutative solitons on a noncommutative torus and their application to tachyon condensation. In the large B limit, they can be exactly described by the Powers-Rieffel projection operators known in the mathematical literature. The resulting soliton spectrum is consistent with T-duality and is surprisingly interesting. It is shown that an instability arises for any D-branes, leading to the decay into many smaller D-branes. This phenomenon is the consequence of the fact that K-homology for type II von Neumann factor is labeled by R.