Polynomial formulations and renormalizability in quantum gravity

Abstract

Non-renormalizability of quantum gravity is traced, in the "binomial" first order metric formulation, to a mismatch between the symmetries of its quadratic and cubic terms, which makes this ostensibly renormalizable system ill-defined about zero vacuum, and forces the usual expansion of the metric about a background. How it might have been is illustrated by the exception, D=2, where the theory is well-defined and hence is "off-shell" finite. In D=3, where the first order vielbein form is also quadratic plus cubic, it is explicitly shown to remain off-shell finite even about non-zero backgrounds, in contrast to the infinities expected in the metric description.

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