[Paper Review] Strongly and slightly flavored gauge theories

Elisabetta Pallante|arXiv (Cornell University)|Dec 28, 2009

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper investigates the phase diagram of non-Abelian gauge theories by varying fermion flavor content, focusing on the emergence of conformal symmetry before the loss of asymptotic freedom. Using lattice simulations and theoretical analysis, it identifies critical flavor thresholds for conformal windows in both strongly and slightly flavored theories, particularly highlighting $SU(3)$ with sextet fermions and $SU(2)$ with adjoint fermions as candidates for near-conformal or walking technicolor behavior.

ABSTRACT

We review some recent progress in our understanding of the phase diagram of non abelian gauge theories, by varying their flavor content -- fermion representations and the number of flavors. In particular, we explore the way conformal symmetry can be restored before the loss of asymptotic freedom, and through a subtle interplay of perturbation theory, chiral dynamics and confining forces. It is with the combination of numerical lattice studies and theoretical insights into gauge theories with and without supersymmetry that we may successfully attempt to clarify the missing pieces of this puzzle.

Motivation & Objective

• To map the phase diagram of non-Abelian gauge theories by varying flavor content, gauge group, and fermion representations.
• To understand the interplay between perturbative renormalization group flow, chiral dynamics, and confining forces in the emergence of conformal symmetry.
• To identify the boundaries of the conformal window—especially the lower end—where conformality may be restored before asymptotic freedom is lost.
• To assess the viability of near-conformal or walking technicolor scenarios in theories with adjoint or higher-representation fermions.
• To connect theoretical findings to phenomenological models beyond the Standard Model and to LHC physics, particularly in electroweak symmetry breaking mechanisms.

Proposed method

• Analyzes the two-loop Callan-Symanzik beta function to determine the running of the gauge coupling and locate the onset of asymptotic freedom loss.
• Applies lattice gauge theory simulations to study non-perturbative dynamics, including screening masses, pseudoscalar decay constants, and the deconfinement transition.
• Uses the discrete beta function and finite-size scaling to probe the existence of an infrared fixed point (IRFP) in $SU(3)$ with two sextet fermions.
• Employs the gap equation and deformation theory to analytically estimate the lower bound of the conformal window, comparing with lattice results.
• Investigates volume independence in the large-$N$ limit for $SU(N)$ with adjoint fermions, testing the feasibility of single-site lattice reductions.
• Combines gluonic and mesonic observables in lattice studies to distinguish between confining and conformal phases in $SU(2)$ with two adjoint Dirac fermions.

Experimental results

Research questions

• RQ1 What is the critical number of flavors $N_f$ at which conformality emerges in $SU(3)$ gauge theories with fundamental or higher-representation fermions?
• RQ2 How does the interplay between chiral dynamics and confining forces affect the stability and location of the conformal window?
• RQ3 Can lattice simulations distinguish between a true infrared fixed point and a walking behavior in $SU(2)$ with two adjoint fermions?
• RQ4 To what extent does the large-$N$ limit lead to volume independence, enabling simplified lattice studies of strongly coupled gauge theories?
• RQ5 What is the connection between the conformal window and phenomenological models such as walking technicolor, and how might this relate to LHC physics?

Key findings

• For $SU(3)$ with two sextet (2S) fermions, lattice evidence supports the existence of an infrared fixed point, suggesting a conformal window near $N_f = 2$.
• The lower end of the conformal window for $SU(3)$ with fundamental fermions is estimated to be around $N_f^c \simeq 2.5$ via gap equation and deformation theory, while asymptotic freedom is lost at $N_f^{AF} = 3$.
• Lattice studies of $SU(2)$ with two Dirac adjoint fermions show hints of conformal or near-conformal behavior, with RG flow and spectrum analysis supporting this scenario.
• Evidence for volume independence in the large-$N$ limit is found in $SU(N)$ with adjoint fermions, supporting the possibility of single-site lattice calculations.
• The phase diagram of $SU(3)$ with fundamental fermions shows a critical line of chiral phase transitions ending at a conformal window boundary, with the window extending to $N_f \approx 16.5$ before loss of asymptotic freedom.
• The study of $SU(2)$ with one adjoint fermion in the large-$N$ limit suggests non-perturbative equivalence to supersymmetric Yang-Mills, indicating potential for simplified dynamics.