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arXiv · 2510.17615

Equivalence of first and second order formulations of the Einstein-Hilbert theory

F. T. Brandt·J. Frenkel·S. Martins-Filho·D. G. C. McKeon
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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.

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F. T. Brandt, J. Frenkel, S. Martins-Filho, D. G. C. McKeon. 2025-10-20. Equivalence of first and second order formulations of the Einstein-Hilbert theory. https://doi.org/10.1103/x6h1-bg4n

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