Equivalence of first- and second-order formulations of the Einstein-Hilbert theory
Phys. Rev. D 113, 026001 – Published 2 January, 2026
DOI: https://doi.org/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.
