Equivalence of first and second order formulations of the Einstein-Hilbert theory
arXiv:2510.17615 · doi:10.1103/x6h1-bg4n
Abstract
We derive a general relation between the background effective actions, which directly proves that the two formulations of the Einstein-Hilbert theory with background fields are equivalent at the quantum level. This basic result has been substantiated in a general background gauge, by explicit calculations at one-loop order of the corresponding counterterm Lagrangians.
21 pages, 2 figures
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