English

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

High Energy Physics - Theory 2026-01-13 v2

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.

Keywords

Cite

@article{arxiv.2510.17615,
  title  = {Equivalence of first and second order formulations of the Einstein-Hilbert theory},
  author = {F. T. Brandt and J. Frenkel and S. Martins-Filho and D. G. C. McKeon},
  journal= {arXiv preprint arXiv:2510.17615},
  year   = {2026}
}

Comments

21 pages, 2 figures