Renormalizability of Quantum Gravity near Two Dimensions

TL;DR

This paper investigates the renormalizability of quantum gravity near two dimensions, demonstrating that counter terms can be absorbed into coupling and wave function renormalizations, preserving diffeomorphism invariance.

Contribution

It proves to all orders that the counter terms in quantum gravity near two dimensions can be absorbed into renormalizations, maintaining full diffeomorphism invariance.

Findings

Counter terms can be absorbed by renormalizations.

Full diffeomorphism invariance is preserved.

Renormalizability is established near two dimensions.

Abstract

We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from the full diffeomorphism invariance. We study the Ward-Takahashi identities to determine the general structure of the counter terms. We prove to all orders that the counter terms can be supplied by the coupling and the wave function renormalization of the tree action. The bare action can be constructed to be the Einstein action form which ensures the full diffeomorphism invariance.