String field theory at large B-field and noncommutative geometry

TL;DR

The paper investigates the exact minimum of the tachyon potential in Witten's cubic string field theory by examining the large $B$-field limit, uncovering a factorized algebra ${\cal A} = {\cal A}_0 \otimes {\cal A}_1$ and connecting D-brane decays to algebraic K-theory on the noncommutative plane and torus. It derives a simpler, operator-based version of Witten's factorization, analyzes projector-based solitons (GMS on the plane and Powers–Rieffel on the torus) with action values that reproduce brane tensions, and links the action to a secondary Chern-Simons class of the associated noncommutative bundles. The authors propose an exact tachyon potential solution via a nonunitary isometry that would relate different vacua through an ansatz $A_0 = V^\dagger * Q V$, while acknowledging possible associativity anomalies and the need for numerical verification. Overall, the work strengthens the bridge between open string field theory, noncommutative geometry, and K-theory, providing a concrete route toward an exact description of tachyon condensation in a large $B$-field regime.

Abstract

In the search for the exact minimum of the tachyon potential in the Witten's cubic string field theory we try to learn as much as possible from the string field theory in the large B-field background. We offer a simple alternative proof of the Witten's factorization, carry out the analysis of string field equations also for the noncommutative torus and find some novel relations to the algebraic K-theory. We note an intriguing relation between Chern-Simons and Chern classes of two noncommutative bundles. Finally we observe a certain pattern which enables us to make a plausible conjecture about the exact form of the minimum.