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 ${\gamma }_m$ 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 ${\gamma }_m^{\star }\approx 0.25$. 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.

Comments: 7 pages, 3 figures