The Generalized Uncertainty Principle. Massless QED Renormalization
Abstract
The effective-field-theory interpretation of generalized uncertainty principle (GUP) deformations does not by itself establish whether their tree-level operator content is closed under renormalization. We investigate this question in massless GUP-deformed quantum electrodynamics at one loop and to first order in the deformation parameter. We compute the ultraviolet divergences of the relevant Green functions and determine the counterterm structure. Our central result is that, after eliminating redundant operators, renormalization requires only one independent physical counterterm beyond those associated with the tree-level theory: an axial-axial four-fermion interaction. The original deformation therefore admits a minimal radiative completion at this order. We derive the leading logarithmic running of the induced Wilson coefficient and discuss its operator-level correspondence with the contact interaction arising in Einstein-Cartan gravity.
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BibTeX
@misc{valero2026generalized,
title = {{The Generalized Uncertainty Principle. Massless QED Renormalization}},
author = {Ezequiel Valero and Héctor Gisbert and Victor Ilisie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24817},
eprint = {2609.24817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24817},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The Generalized Uncertainty Principle. Massless QED Renormalization
AU - Ezequiel Valero
AU - Héctor Gisbert
AU - Victor Ilisie
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24817
UR - https://arxiv.org/abs/2609.24817
AB - The effective-field-theory interpretation of generalized uncertainty principle (GUP) deformations does not by itself establish whether their tree-level operator content is closed under renormalization. We investigate this question in massless GUP-deformed quantum electrodynamics at one loop and to first order in the deformation parameter. We compute the ultraviolet divergences of the relevant Green functions and determine the counterterm structure. Our central result is that, after eliminating redundant operators, renormalization requires only one independent physical counterterm beyond those associated with the tree-level theory: an axial-axial four-fermion interaction. The original deformation therefore admits a minimal radiative completion at this order. We derive the leading logarithmic running of the induced Wilson coefficient and discuss its operator-level correspondence with the contact interaction arising in Einstein-Cartan gravity.
ER -