  A famous conjecture of Artin states that there are infinitely many prime
numbers for which a fixed integer $g$ is a primitive root, provided $g \neq -1$
and $g$ is not a perfect square. Thanks to work of Hooley, we know that this
conjecture is true, conditional on the truth of the Generalized Riemann
Hypothesis. Using a combination of Hooley's analysis and the techniques of
Maynard-Tao used to prove the existence of bounded gaps between primes, Pollack
has shown that (conditional on GRH) there are bounded gaps between primes with
a prescribed primitive root. In the present article, we provide an
unconditional proof of the analogue of Pollack's work in the function field
case; namely, that given a monic polynomial $g(t)$ which is not an $v$th power
for any prime $v$ dividing $q-1$, there are bounded gaps between monic
irreducible polynomials $P(t)$ in $\mathbb{F}_q[t]$ for which $g(t)$ is a
primitive root (which is to say that $g(t)$ generates the group of units modulo
$P(t)$). In particular, we obtain bounded gaps between primitive polynomials,
corresponding to the choice $g(t) = t$.
