2020/07/31 by Shira Chapman, Lorenzo Di Pietro, Kevin T. Grosvenor +1 · 1 citation
Physics and Astronomy · #hep-th #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1007/jhep10(2020)195
27+10 pages, 5 figures; v2: minor corrections, references added
arxiv created 2021/03/15 · arxiv updated 2021/03/17
We study the quantum properties of a Galilean-invariant abelian gauge theory coupled to a Schrödinger 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 Lévy-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.