Star Products from Commutative String Theory

TL;DR

This paper derives derivative corrections to the Chern-Simons coupling in string theory, showing they sum into a star product structure consistent with noncommutative predictions, in a B-field background.

Contribution

It provides a boundary-state computation of derivative corrections that sum into a star product, linking commutative and noncommutative descriptions in string theory.

Findings

Corrections sum into a *2 product of gauge fields

Results agree with noncommutative predictions

Analysis performed in a constant B-field background

Abstract

A boundary-state computation is performed to obtain derivative corrections to the Chern-Simons coupling between a p-brane and the RR gauge potential C(p-3). We work to quadratic order in the gauge field strength F, but all orders in derivatives. In a certain limit, which requires the presence of a constant B-field background, it is found that these corrections neatly sum up into the *2 product of (commutative) gauge fields. The result is in agreement with a recent prediction using noncommutativity.