Recent applications of the gradient flow
Abstract
The gradient flow provides a gauge- and O(4)-invariant ultraviolet regulator for QCD. This opens new opportunities for combining non-perturbative lattice calculations with perturbative results, in particular in the context of an operator-product expansion (OPE). We review the concepts behind this and argue that, within the operator basis of a given OPE, the flow-time dependence of the conversion between flowed and regular Wilson coefficients is exact at each perturbative order. Recent applications to parton distribution functions, heavy-meson observables, quark masses, and gradient-flow definitions of the strong coupling are discussed. Finally, the perturbative formulation of the Ricci flow in quantum gravity and its application to the study of non-Gaussian fixed points is reviewed.
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BibTeX
@misc{harlander2026recent,
title = {{Recent applications of the gradient flow}},
author = {R. Harlander and A. Shindler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07940},
eprint = {2609.07940},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07940},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Recent applications of the gradient flow
AU - R. Harlander
AU - A. Shindler
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07940
UR - https://arxiv.org/abs/2609.07940
AB - The gradient flow provides a gauge- and O(4)-invariant ultraviolet regulator for QCD. This opens new opportunities for combining non-perturbative lattice calculations with perturbative results, in particular in the context of an operator-product expansion (OPE). We review the concepts behind this and argue that, within the operator basis of a given OPE, the flow-time dependence of the conversion between flowed and regular Wilson coefficients is exact at each perturbative order. Recent applications to parton distribution functions, heavy-meson observables, quark masses, and gradient-flow definitions of the strong coupling are discussed. Finally, the perturbative formulation of the Ricci flow in quantum gravity and its application to the study of non-Gaussian fixed points is reviewed.
ER -