Abstract
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. 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 function of the fermion mass. Finally, for the first time, we extend the instanton calculus to asymptotically safe theories.
Highlights
The standard model and its four-dimensional extensions are described by gauge-Yukawa theories; it is paramount to understand their dynamics.Of special interest are theories that are fundamental according to Wilson [1,2], meaning that they are well defined at arbitrarily short distances
We investigate the instanton dynamics of asymptotically safe and free quantum field theories featuring, respectively, controllable ultraviolet and infrared fixed points
The above discussion leads us to look for the solution below the energy scale m, where running of the couplings is given by pure YM beta functions
Summary
The standard model and its four-dimensional extensions are described by gauge-Yukawa theories; it is paramount to understand their dynamics. The infrared dynamics of fundamental field theories is extremely rich, and it can entail confinement and/or chiral symmetry breaking or large distance conformality This depends on the field content of the specific quantum field theory as well as the presence and type of infrared relevant operators such as scalar and fermion masses. We are concerned with generalizing and applying the instanton calculus to gauge theories in the perturbative regime of the QCD conformal window as well as of controllable nonsupersymmetric asymptotically safe quantum field theories [5,6]. We compute the density of instantons per unit volume as a function of the fermion mass measured in units of the RG invariant scale The latter separates the infrared interacting theory from the UV free fixed point.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
