Beyond Miransky Scaling

TL;DR

This paper investigates how the scaling behavior of physical observables near a quantum critical point in many-flavor QCD is modified by the running of the gauge coupling, revealing universal power-law corrections to Miransky scaling.

Contribution

It derives universal power-law corrections to Miransky scaling considering the scale dependence of the gauge coupling and illustrates them using nonperturbative functional renormalization group methods.

Findings

Universal power-law corrections are derived for Miransky scaling.

Corrections are determined by the IR critical exponent of the gauge coupling.

Power-law scaling becomes more relevant at specific flavor numbers in lattice simulations.

Abstract

We study the scaling behavior of physical observables in strongly-flavored asymptotically free gauge theories, such as many-flavor QCD. Such theories approach a quantum critical point when the number of fermion flavors is increased. It is well-known that physical observables at this quantum critical point exhibit an exponential scaling behavior (Miransky scaling), provided the gauge coupling is considered as a constant external parameter. This scaling behavior is modified when the scale dependence of the gauge coupling is taken into account. Provided that the gauge coupling approaches an IR fixed point, we derive the resulting universal power-law corrections to the exponential scaling behavior and show that they are uniquely determined by the IR critical exponent of the gauge coupling. To illustrate our findings, we compute the universal corrections in many-flavor QCD with the aid of nonperturbative functional renormalization group methods. In this case, we expect the power-law scaling to be quantitatively more relevant if the theories are probed, for instance, at integer Nf as done in lattice simulations.