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arXiv · hep-th/9307131

On the stability of renormalizable expansions in three-dimensional gravity

Shun'ya Mizoguchi·Hisashi Yamamoto
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Abstract

Preliminary investigations are made for the stability of the $1/N$ expansion in three-dimensional gravity coupled to various matter fields, which are power-counting renormalizable. For unitary matters, a tachyonic pole appears in the spin-2 part of the leading graviton propagator, which implies the unstable flat space-time, unless the higher-derivative terms are introduced. As another possibility to avoid this spin-2 tachyon, we propose Einstein gravity coupled to non-unitary matters. It turns out that a tachyon appears in the spin-0 or -1 part for any linear gauges in this case, but it can be removed if non-minimally coupled scalars are included. We suggest an interesting model which may be stable and possess an ultraviolet fixed point.

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Shun'ya Mizoguchi, Hisashi Yamamoto. 1994-09-26. On the stability of renormalizable expansions in three-dimensional gravity. https://doi.org/10.1103/physrevd.50.7351

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