String field theory at large B-field and noncommutative geometry

TL;DR

This paper explores string field theory in large B-field backgrounds, revealing new algebraic relations, analyzing equations on noncommutative tori, and proposing a conjecture for the tachyon potential minimum.

Contribution

It provides an alternative proof of Witten's factorization, analyzes string equations on noncommutative tori, and uncovers novel links to algebraic K-theory and noncommutative geometry.

Findings

New relations between Chern-Simons and Chern classes in noncommutative bundles

Analysis of string field equations on noncommutative tori

A plausible conjecture for the exact minimum of the tachyon potential

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.