Renormalizability of Quantum Gravity 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.

26 pages, Latex file, No figures

References in corpus (8)

• Scaling Exponents in Quantum Gravity near Two Dimensions
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• Renormalization of gauge invariant operators and anomalies in Yang-Mills theory
• Local BRST cohomology in Einstein--Yang--Mills theory
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