Conformal window from conformal expansion
Non-abelian gauge theories coupled to fermion matter, such as quantum chromodynamics (QCD), have played a prominent role in particle and nuclear physics for the last several decades. In recent days, our interests in these theories have diversified as they can serve as ultra-violet complete models in the context of physics beyond the standard model. If the theory is asymptotically free, a particularly interesting question related with such model buildings is whether it is confined or conformal in the infra-red. In this talk, we will discuss the underlying mechanism responsible for the quantum phase transition between the two phases and argue that it can be characterized by a critical condition to the anomalous dimension of a fermion bilinear operator. Then, we compute the anomalous dimension by exploiting the Banks-Zaks conformal expansion and estimate the conformal window in which the theory is infra-red conformal by using the critical condition at finite order. We attempt to calculate the theory errors associated with the truncation of the conformal expansion by treating its large-order behavior separately, either convergent or divergent asymptotic. We critically assess our results by comparing to other analytical methods as well as lattice results available in the literature.
Coming Soon!