  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 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 gauge theory, namely the scalar QED which has
a $U(1)$ gauge field interacting with critical bosons. In $d=2+\epsilon$
dimensions we successfully solve it by obtaining a kink as well as an island of
the scalar QED. Further attempt towards the $3d$ scalar QED is also discussed.
