Anomalous dimensions on the lattice

Abstract

We review methods and results for extracting the anomalous dimensions of operators from lattice field theory calculations. The most important application is the anomalous mass dimension in conformal or nearly conformal gauge field theories which might be related to dynamical electroweak symmetry breaking. Some discussion of the underlying theory of renormalization and mixing of operators is also included.

54 pages, 4 figures

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• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Higher-Order Scheme-Independent Series Expansions of ${\gamma }_{\bar{\psi }\psi ,IR}$ and ${\beta }_{IR}^{\prime }$ in Conformal Field Theories
• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Anomalous Dimensions of Conformal Baryons
• Large mass hierarchies from strongly-coupled dynamics
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach
• Proof of the renormalizability of the gradient flow
• The spectrum and mass anomalous dimension of SU(2) adjoint QCD with two Dirac flavours
• Lattice Gauge Theory for Physics Beyond the Standard Model
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory
• Effective field theory for pions and a dilatonic meson
• Novel Approaches to Renormalization Group Transformations in the Continuum and on the Lattice
• Measurement of the mass anomalous dimension of near-conformal adjoint QCD with the gradient flow