Investigating the critical properties of beyond-QCD theories using Monte Carlo Renormalization Group matching

TL;DR

This paper applies Monte Carlo Renormalization Group matching to study the phase structure of SU(3) gauge theories with different flavor numbers, identifying fixed points and critical exponents non-perturbatively.

Contribution

It demonstrates how 2-lattice matching MCRG methods can predict fixed points and critical behavior in beyond-QCD theories, including the identification of an infrared fixed point at Nf=16.

Findings

Pure gauge and Nf=4 models are confining and chirally broken.

Nf=16 model shows an infrared fixed point with nearly marginal coupling.

Preliminary results on the scaling dimension of mass at the fixed point.

Abstract

Monte Carlo Renormalization Group (MCRG) methods were designed to study the non-perturbative phase structure and critical behavior of statistical systems and quantum field theories. I adopt the 2-lattice matching method used extensively in the 1980's and show how it can be used to predict the existence of non-perturbative fixed points and their related critical exponents in many flavor SU(3) gauge theories. This work serves to test the method and I study relatively well understood systems: the $N_f=0$, 4 and 16 flavor models. The pure gauge and $N_f=4$ systems are confining and chirally broken and the MCRG method can predict their bare step scaling functions. Results for the $N_f=16$ model indicate the existence of an infrared fixed point with nearly marginal gauge coupling. I present preliminary results for the scaling dimension of the mass at this new fixed point.