Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories (0901.3766v2)

Abstract: Using lattice simulations, we study the extent of the conformal window for an SU(3) gauge theory with N_f Dirac fermions in the fundamental representation. We extend our recently reported work, describing the general framework and the lattice simulations in more detail. We find that the theory is conformal in the infrared for N_f = 12, governed by an infrared fixed point, whereas the N_f = 8 theory exhibits confinement and chiral symmetry breaking. We therefore conclude that the low end of the conformal window N_f^c lies in the range 8 <= N_f^c <= 12. We discuss open questions and the potential relevance of the present work to physics beyond the standard model.

Analysis of Lattice SU(3) Yang-Mills Conformal Behavior

The study presented in the paper "Lattice study of conformal behavior in SU$(3)$ Yang-Mills theories" provides an in-depth exploration of the conformal window in SU(3) gauge theories with varying numbers of Dirac fermions ($N_f$) in the fundamental representation. Through extensive lattice simulations, the authors use the Schrödinger functional (SF) method to derive a gauge-invariant, nonperturbative running coupling, probing the conformal behavior of these theories in the infrared limit.

Key Numerical Results and Claims

• Conformal Window Boundaries: The lattice simulations suggest that the lower end of the conformal window for SU(3) lies between $8 \leq N_f^c \leq 12$. Specifically, for $N_f=12$, the theory appears conformal in the infrared, governed by an infrared fixed point. In contrast, for $N_f=8$, the simulations find evidence of confinement and chiral symmetry breaking, with no indication of an infrared fixed point.
• Running Coupling and Fixed Points: The results indicate that for $N_f=12$, despite the presence of an infrared fixed point, the value of the fixed point remains below the threshold required for triggering chiral symmetry breaking, consistent with estimates based on perturbative approaches. The simulations show reasonable agreement with the three-loop perturbative results within the three-loop scheme, supporting the existence of a fixed point for $N_f=12$.

Theoretical and Practical Implications

This work has important implications for theoretical physics, particularly in exploring phases of gauge theories that could have novel behavior distinct from standard QCD-like theories. The existence of a conformal window in non-supersymmetric theories is crucial for understanding the dynamics of gauge theories not described by the standard model.

In the context of physics beyond the standard model, such theories could find relevance in the formulation of "walking" technicolor models, wherein the gauge dynamics provides a mechanism for electroweak symmetry breaking without elementary Higgs fields. The observed lower bound of the conformal window, specifically the transition from conformal to confining behavior, is significant for identifying viable candidate theories.

Future Directions

Further research directions could include simulations for intermediate values of $N_f$ (e.g., $N_f=10$) to refine the boundary of the conformal window and the nature of the transition into the confining phase. Comparing results with other schemes, such as those based on Wilson loops or static potentials, may provide additional nonperturbative evidence for the results presented.

This lattice approach opens new pathways for studying other representations of fermions or different gauge groups, potentially broadening the understanding of gauge theories with varied representations or dimensions.

The paper showcases how nonperturbative lattice simulations can effectively explore the complex phase structure of gauge theories, underlining the necessity of such approaches in theoretical physics. Given the implications for models beyond the standard model, these findings contribute significantly to the ongoing discourse on the nature and dynamics of gauge theories in the conformal window.