  Wetterich's equation provides a powerful tool for investigating the existence
and universal properties of renormalization group fixed points exhibiting
quantum scale invariance. Motivated by recent works on asymptotically safe
scalar-tensor theories, we develop a novel approximation scheme which projects
the functional renormalization group equation onto functions of the kinetic
term. Applying this projection to scalars and gauge fields, our analysis
identifies a new universality class with a very special spectrum of stability
coefficients. The implications of our findings in the context of asymptotically
safe gravity-matter systems are discussed.
