TL;DR
This paper reviews the ultraviolet divergences in local quantum gravity theories, including supergravity, and presents recent findings that even the highest-dimensional supergravity model exhibits infinities at two loops, challenging the viability of quantum gravity models.
Contribution
It provides a comprehensive review of ultraviolet issues in quantum gravity and reports new results showing divergences in D=11 supergravity at two loops.
Findings
Ultraviolet divergences are present in Einstein and supergravity theories.
D=11 supergravity exhibits infinities at 2 loops.
No viable nonghost quantum field model includes general relativity.
Abstract
We first present a review, intended for classical relativists, of the ultraviolet difficulties faced by local quantum gravity theories in both the usual Einstein versions and in their supergravity extensions, at least perturbatively. These problems, present in arbitrary dimensions, are traceable to the dimensionality of the Einstein constant. We then summarize very recent results about supergravity at the highest allowed dimension, D=11, showing that also this unique model suffers from infinities already at 2 loops, despite its high degree of supersymmetry. The conclusion is that there is no viable nonghost quantum field model that includes general relativity.
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