Gauge fields on $B$-branes over ${\mathbb{C}\mathbb{P}}^n$

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 ${\mathcal{G}}^{\bullet }$ is $\le 1$. Moreover, the cardinal is $1$ iff each ${\mathcal{G}}^p$ is isomorphic to a direct sum of copies of ${\mathcal{O}}_{{\mathbb{P}}^n}$.