  How many charged degrees of freedom are necessary to accommodate a certain
amount of 't Hooft anomaly? Using the conformal bootstrap for the four-point
function of flavor current multiplets, we show that in all (3+1)d
superconformal field theories the 't Hooft anomaly of a continuous flavor
symmetry is bounded from above by the 3/2 power of the current two-point
function coefficient, which can be thought of as a measure for the amount of
charged degrees of freedom. We check our bounds against free fields and SQCD in
the conformal window.
