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arXiv · 1311.1287

Determining the mass anomalous dimension through the eigenmodes of Dirac operator

Anqi Cheng·Anna Hasenfratz·Gregory Petropoulos·David Schaich
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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.

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Anqi Cheng, Anna Hasenfratz, Gregory Petropoulos, David Schaich. 2013-11-06. Determining the mass anomalous dimension through the eigenmodes of Dirac operator. https://doi.org/10.22323/1.187.0088

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