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arXiv · hep-th/9303006

Quantum $R^2$ Gravity in Two Dimensions

Hikaru Kawai·Ryuichi Nakayama
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Abstract

Two-dimensional quantum gravity with an $R^2$ term is investigated in the continuum framework. It is shown that the partition function for small area $A$ is highly suppressed by an exponential factor $exp \{ -2π(1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32π$) of $R^2$ and $h$ is the genus of the surface. Although positivity is violated, at a short distance scale ( $\ll 1/m$) surfaces are smooth and the problem of the branched polymer is avoided.

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Hikaru Kawai, Ryuichi Nakayama. 1993-03-02. Quantum $R^2$ Gravity in Two Dimensions. https://doi.org/10.1016/0370-2693(93)90072-p

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