A roadmap for bootstrapping critical gauge theories: decoupling operators of conformal field theories in $d>2$ dimensions

Understand

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.