Abstract
Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics and derive flow equations for the Wilsonian effective action with the perturbative expansion in the gauge coupling. We focus on the quantum corrections to the correlation functions up to the second order of the gauge coupling and discuss the gauge invariance of the GF-ERG flow. We demonstrate that the anomalous dimension of the gauge field agrees with the standard perturbative computation and that the mass of the photon keeps vanishing in general spacetime dimensions. The latter is a noteworthy fact that contrasts with the conventional Exact Renormalization Group formalism in which an artificial photon mass proportional to a cutoff scale is induced. Our results imply that the GF-ERG can give a gauge-invariant renormalization group flow in a non-perturbative way.
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Acknowledgments
The authors thank Jan M. Pawlowski for intensive discussions at the initial stage of this work and for carefully reading our manuscript. J. H. acknowledges the Institute for Theoretical Physics, Heidelberg University, for the very kind hospitality during his stay. The authors also thank Hiroshi Suzuki for valuable discussions and comments. In particular, the proof of the vanishing 1-loop contribution to the photon mass is inspired by the discussion in the QED case with him. J. H. thanks the members of the Elementary Particle Theory Group at Kyushu University for their hospitality during his stay. The work of J. H. is partially supported by JSPS Grant-in-Aid for Scientific Research KAKENHI Grant No. JP21J14825. The work of M. Y. is supported by the National Science Foundation of China (NSFC) under Grant No. 12205116 and the Seeds Funding of Jilin University.
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Haruna, J., Yamada, M. Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics. J. High Energ. Phys. 2024, 291 (2024). https://doi.org/10.1007/JHEP05(2024)291
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DOI: https://doi.org/10.1007/JHEP05(2024)291