Quantum $R^2$ Gravity in Two Dimensions

Details Quantum $R^2$ Gravity in Two Dimensions Quantum $R^2$ Gravity in Two Dimensions

1993-03-02

arxiv.org/abs/hep-th/9303006v1

Phys.Lett. B306 (1993) 224-232

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, latex KEK-TH-355, KEK preprint 92-212, UT-634

Scientific paper

10.1016/0370-2693(93)90072-P

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 $exp \{ -2\pi (1-h)^2/(m^2A) \}$, where $1/m^2$ is the coefficient (times $32\pi$) 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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