4 D Quantum N-Dilaton Gravity and One-Loop Divergence of Effective Action on Constant Dilaton

TL;DR

This paper analyzes the one-loop divergences in 4D quantum gravity coupled with N-dilatons, revealing the structure of divergences, coupling constraints, and the non-renormalizability for N ≥ 1.

Contribution

It provides a detailed analysis of divergence structures and coupling constraints in 4D N-dilaton gravity on constant dilaton backgrounds, highlighting non-renormalizability issues.

Findings

Divergent terms structure on constant dilaton backgrounds.

Coupling constraints to cancel Weyl tensor divergences.

Non-renormalizability for N ≥ 1 due to persistent divergences.

Abstract

We consider 4D quantum gravity with N-dilatons with the most general couplings. Especially, on constant dilaton and arbitrary metric background, we show the structure of the divergent terms. We show the constraint between the couplings necessary to cancel the coefficient of the square of the Wyle tensor. Next we show the N dependence of a non-renormalizable divergent term, and found that it cannot be canceled in the case of $N \geq 1$ with any fine-tuning of the couplings.