$\mathrm{\Lambda }$-symmetry and background independence of noncommutative gauge theory on ${\mathbb{R}}^n$

Background independence of noncommutative Yang-Mills theory on ${\mathbb{R}}^n$ is discussed. The quantity $\theta \widehat{F}\theta -\theta$ is found to be background dependent at subleading order, and it becomes background independent only when the ordinary gauge field strength $F$ is constant. It is shown that, at small values of $B$, the noncommutative Dirac-Born-Infeld action possesses $\mathrm{\Lambda }$-symmetry at least to subleading order in $\theta$ if $F$ damps fast enough at infinity.