Determining the mass anomalous dimension through the eigenmodes of Dirac operator

Abstract

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 γm of an asymptotically-free system to the universal γ?m 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 484. 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 γ?m ≈ 0.25. Our method provides a unique probe to study systems from the UV to the IR. It is universal and can be applied to any lattice model of interest, including both chirally-broken and IR-conformal systems.