Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1204.4432

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

Agostino Patella
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Agostino Patella. 2012-08-17. A precise determination of the psibar-psi anomalous dimension in conformal gauge theories. https://doi.org/10.1103/physrevd.86.025006

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Decomposition of the axial-vector current in a finite box

We consider the matrix element of the axial-vector current between two nucleon states in a finite box. Starting from the chiral Lagrangian density with nucleon and Delta-isobar degrees of freedom, we study the finite-volume effects at the one-loop level. We show that the standard decomposition into the axial-vector and pseudoscalar form factor is incomplete in a finite box. We derive expressions for the complete set of in-box form factors at one loop, and demonstrate how to extract the full set from lattice correlation functions. We verify that the axial Ward identity holds in the chiral limit. We derive the one-loop expressions for the pseudoscalar form factor and verify that the in-box axial Ward identity away from the chiral limit is fulfilled also. Selected numerical results are shown for two flavor-SU(2) lattice ensembles. Sizable finite-volume effects are observed, with an important role for the Delta-isobar. We discuss the implications of our results for lattice studies of the axial-vector current. We conclude that full finite-box results are crucial for a precise determination of the form factors.

hep-lat↗
arXiv2026

A variational framework for variance reduction in lattice field theory

The signal-to-noise problem limits the reach of many lattice calculations. We present a variational framework that recasts it as a transport problem: the loss of signal reflects a mismatch between the distribution one samples and the one needed to measure an observable, and can be reduced by transporting configurations to close that gap. The optimal transport is typically determined either through a stochastic estimator based on Langevin dynamics or by parametrising it as a normalising flow trained with automatic differentiation. We discuss how the framework brings these methods under a common variational principle and present results for scalar theories.

hep-lat↗
arXiv2026

Larger physical volume and bounds on the number of matter fields in noncompact gauge theories on a lattice

The work was motivated by the numerical result that in a pure SU(2) gauge theory the ratio R of the effective non-compact and compact lattice spacing is larger than 1 and increasing with decreasing gauge coupling, as well as the expectation that it should further increase extending the parameter space. This means that with a noncompact regularization, at given number of lattice sites and comparable scaling, one can obtain a larger physical volume, whose importance for the control of size effects has long been known. We confirm qualitatively results and expectation by a perturbative evaluation of the effective lattice spacing in an expansion in the Plank constant of non-compact pure SU(2) and Abelian gauge theories, but we find in addition that R reaches the maximum value of sqrt(2). Including matter fields we find that R increases ( still up to sqrt(2) ) or decreases depending on the difference between the number of scalar and spinor degrees of freedom, and there are bounds on such a difference.

hep-lat↗