A precise determination of the psibar-psi anomalous dimension in conformal gauge theories

Abstract

A strategy for computing the psibar-psi anomalous dimension at the fixed point in infrared-conformal gauge theories from lattice simulations is discussed. The method is based on the scaling of the spectral density of the Dirac operator or rather its integral, the mode number. It is relatively cheap, mainly for two reasons: (a) the mode number can be determined with quite high accuracy, (b) the psibar-psi anomalous dimension is extracted from a fit of several observables on the same set of configurations (no scaling in the Lagrangian parameters is needed). As an example the psibar-psi anomalous dimension has been computed in the SU(2) theory with 2 Dirac fermions in the adjoint representation of the gauge group, and has been found to be 0.371(20). In this particular case, the proposed strategy has proved to be very robust and effective.

LaTeX, 16 pages, 3 PDF figures, [v3] minor cosmetic changes

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• Exploring gauge theories with adjoint matter on the lattice
• Determination of the mass anomalous dimension for $N_f=12$ and $N_f=9$ SU($3$) gauge theories
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• Eigenvalue spectrum and scaling dimension of lattice $\mathcal{N}=4$ supersymmetric Yang-Mills
• Adjoint SU(2) with Four Fermion Interactions
• SU(2) gauge theory with one and two adjoint fermions towards the continuum limit
• Exploring conformality in lattice N=4 supersymmetric Yang--Mills
• Measurement of the mass anomalous dimension of near-conformal adjoint QCD with the gradient flow