Infrared fixed point of the SU(3) gauge theory with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>10</mml:mn></mml:math> flavors
Anna Hasenfratz, Ethan T. Neil, Yigal Shamir, Benjamin Svetitsky, Oliver Witzel
Abstract
We use lattice simulations and the continuous renormalization group method, based on the gradient flow, to calculate the $\ensuremath{\beta}$ function and anomalous dimensions of the SU(3) gauge theory with ${N}_{f}=10$ flavors of fermions in the fundamental representation. We employ several improvements to extend the range of available renormalized couplings, including the addition of heavy Pauli-Villars bosons to reduce cutoff effects and the combination of a range of gradient flow transformations. While in the weak coupling regime our result is consistent with those of earlier studies, our techniques allow us to study the system at much stronger couplings than previously possible. We find that the renormalization group $\ensuremath{\beta}$ function develops a zero, corresponding to an infrared-stable fixed point, at gradient-flow coupling ${g}^{2}=15.0(5)$. We also determine the mass and tensor anomalous dimensions: At the fixed point we find ${\ensuremath{\gamma}}_{m}\ensuremath{\simeq}0.6$, suggesting that this system might be deep inside the conformal window.