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Renormalization of Galilean Electrodynamics

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arxiv 2007.03033 v2 pith:N4CZNNBU submitted 2020-07-06 hep-th cond-mat.quant-gascond-mat.str-el

Shira Chapman , Lorenzo Di Pietro , Kevin T. Grosvenor , Ziqi Yan This is my paper · ORCID
classification hep-thcond-mat.quant-gascond-mat.str-el
keywords theoryfieldgalileanquantumscalarcoupledcouplingdimensions
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We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schr\"odinger scalar in 2+1 dimensions. At the classical level, the theory with minimal coupling is obtained from a null-reduction of relativistic Maxwell theory coupled to a complex scalar field in 3+1 dimensions and is closely related to the Galilean electromagnetism of Le-Bellac and L\'evy-Leblond. Due to the presence of a dimensionless, gauge-invariant scalar field in the Galilean multiplet of the gauge-field, we find that at the quantum level an infinite number of couplings is generated. We explain how to handle the quantum corrections systematically using the background field method. Due to a non-renormalization theorem, the beta function of the gauge coupling is found to vanish to all orders in perturbation theory, leading to a continuous family of fixed points where the non-relativistic conformal symmetry is preserved.

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Cited by 3 Pith papers

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  1. Interacting Galilean and Finite-Energy Carroll Fermions

    hep-th 2026-08 conditional novelty 7.0 of 10

    A c-dependent similarity transformation generates new Galilean and Carrollian fermion actions, including a Carrollian model with non-removable finite energy and a Galilean model with an accidental fermionic gauge symmetry.

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    hep-th 2025-10 conditional novelty 7.0 of 10

    Schrödinger CFTs are reformulated via a harmonic-trap thermofield double, giving a state-operator correspondence for all operators and a factorization proof of non-renormalization.

  3. An Introduction to String Newton-Cartan Holography and Integrability

    hep-th 2026-03 accept novelty 3.0 of 10

    String Newton-Cartan holography, the non-relativistic limit of the AdS/CFT correspondence, is organized and reviewed around five consistency conditions, with its classical solutions, spectrum, and integrability structure.

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