Determining the mass anomalous dimension through the eigenmodes of Dirac operator

Understand

We define a scale-dependent effective mass anomalous dimension from the scaling of the mode number of the massless Dirac operator, which connects the perturbative $\gamma_m$ of an asymptotically-free system to the universal $\gamma_m^{\star}$ at a conformal fixed point.

• We use a stochastic algorithm to measure the mode number up to the cutoff scale on lattices as large as $48^4$.
• Focusing on SU(3) lattice gauge theory with $N_f = 12$ massless fundamental fermions, we examine systematic effects due to finite volumes and non-zero fermion masses.
• Our results suggest the existence of an infrared fixed point with $\gamma_m^{\star} \approx 0.25$.