Renormalization of Einstein gravity through a derivative-dependent field redefinition

Abstract

This work explores an alternative solution to the problem of renormalizability in Einstein gravity. In the proposed approach, Einstein gravity is transformed into the renormalizable theory of four-derivative gravity by applying a local field redefinition containing an infinite number of higher derivatives. It is also shown that the current-current amplitude is invariant with the field redefinition, and thus the unitarity of Einstein gravity is preserved.

Renormalization group in super-renormalizable quantum gravity

“…One can see an example of this procedure described in the recent paper Ref. [76]. This approach to quantum gravity has only three problems: (i) the procedure of changing the field in an arbitrary way is not a change of variables (classical or quantum) and does not belong to the conventional quantum field theory; (ii) in some cases it requires infinitely precise fine-tuning of infinitely many parameters, as it was recently discussed in [40] in relation to string theory and Zwiebach transformation [54]; (iii) there are serious ambiguities in the resulting action since there are many higher derivative terms which do not produce ghosts, and which can be eliminated or not, depending on our will [77].…”

On the equivalence between fR theories and Einstein gravity

“…It is to be noted that under the conformal transformation (12), the coupling of matter with the space-time curvature changes. This is because of the fact that the matter Lagrangian density L m explicitly contains the metric, and any redefinition of the metric will correspondingly feature in L m as well.…”

“…Authors like [12] decided to approach the inverse problem while trying to perturbatively renormalize gravity. They started with GR, and under field redefinition was able to obtain the most general quadratic theory, that is equation (1) truncated till R 2 .…”

Limiting fluctuations in quantum gravity to diffeomorphisms

“…When sources are present, the more general form involving the Jacobian determinant [Eq. (7)] must be used. This determinant also arises in gauge fixing of conformal field theories.…”

“…Since the gravitational coupling constant has units of length, the quantum corrections correspond to higher-derivative terms with divergent coefficients [1][2][3]. At one-loop order, the divergence in pure gravity vanishes on shell, i.e., when the classical equations of motion are imposed on the background fields [1][2][3][4][5][6][7]. However, on-shell divergences appear at two-loop order [8][9][10][11] or when coupled to matter [1,12].…”