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

Abstract

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 ${\mathscr O}_{{\mathbb P}^n}$.