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Gradient flow coupling of three- and four-dimensional QED

Lars Georg, Robert V. Harlander, and Robert H. Mason

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Phys. Rev. D 113, 076016 – Published 16 April, 2026

DOI: https://doi.org/10.1103/n586-vj2q

Abstract

We evaluate the coupling of quantum electrodynamics (QED) in the gradient-flow scheme in three and four space-time dimensions. Our general result applies to any theory with a U(1) gauge field coupled to arbitrary other fields via arbitrary interactions. As an example, we consider QED with nf flavors in three and four space-time dimensions and evaluate the corresponding β functions. In four dimensions, we find that the perturbative expansion of the β function behaves much better than the corresponding expression in quantum chromodynamics. In three dimensions, we recover both the ultraviolet as well as the infrared fixed points of the QED coupling in the large-nf limit.

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Phys. Rev. D 113, 076016– Published 16 April, 2026
  • Received 30 January 2026
  • Accepted 10 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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