  We propose a roadmap for bootstrapping conformal field theories (CFTs)
described by gauge theories in dimensions $d>2$. In particular, we provide a
simple and workable answer to the question of how to detect the gauge group in
the bootstrap calculation. Our recipe is based on the notion of
\emph{decoupling operator}, which has a simple (gauge) group theoretical
origin, and is reminiscent of the null operator of $2d$ Wess-Zumino-Witten CFTs
in higher dimensions. Using the decoupling operator we can efficiently detect
the rank (i.e. color number) of gauge groups, e.g., by imposing gap conditions
in the CFT spectrum. We also discuss the physics of the equation of motion,
which has interesting consequences in the CFT spectrum as well. As an
application of our recipes, we study a prototypical critical gauge theory,
namely the scalar QED which has a $U(1)$ gauge field interacting with critical
bosons. We show that the scalar QED can be solved by conformal bootstrap,
namely we have obtained its kinks and islands in both $d=3$ and $d=2+\epsilon$
dimensions.
