Instantons in asymptotically safe and free quantum field theories

We investigate the instanton dynamics of asymptotically safe and free quantum field theories featuring, respectively, controllable ultraviolet and infrared fixed points. We start by briefly reviewing the salient points about the instanton calculus for pure Yang-Mills (YM) and QCD theory. We then move on to determine the role of instantons within the controllable regime of the QCD conformal window. In this region we add a fermion-mass operator and determine the density of instantons per unit volume as a function of the fermion mass. Finally, for the first time, we extend the instanton calculus to asymptotically safe theories.