  Considering the $B$-branes over the complex projective space ${\mathbb P}^n$
as the objects of the bounded derived category $D^b({\mathbb P}^n)$, we prove
that the cardinal of the set of holomorphic gauge fields on a given $B$-brane
${\mathscr G}^{\bullet}$ is $\leq 1$. Moreover, the cardinal is $1$ iff each
${\mathscr G}^p$ is isomorphic to a direct sum of copies of ${\mathscr
O}_{{\mathbb P}^n}$.
