A Note on Background Independence in Noncommutative Gauge Theories, Matrix Model and Tachyon Condensation

TL;DR

This paper explores background independence in noncommutative gauge theories via D-branes with B fields, linking matrix models, tachyon condensation, and noncommutative geometry to clarify degrees of freedom and description choices.

Contribution

It provides a physical interpretation of background independence in noncommutative gauge theories using matrix models and clarifies the role of the two-form  in different frameworks.

Findings

Background independent variables are identified with matrix model degrees of freedom.

The results extend understanding of tachyon condensation endpoints in B-field D-branes.

The -form parametrizes description freedom in noncommutative geometry and string theory.

Abstract

Using the construction of D-branes with nonzero $B$ field in the matrix model we give a physical interpretation of the known background independence in gauge theories on a noncommutative space. The background independent variables are identified as the degrees of freedom of the underlying matrix model. This clarifies and extends some recent results about the end point of tachyon condensation in D-branes with a $B$ field. We also explain the freedom in the description which is parametrized by a two form $\Phi$ from the points of view of the noncommutative geometry on the worldvolume of the branes, and of the first quantized string theory.