A modified c=1 matrix model with new critical behavior

Details A modified c=1 matrix model with new critical behavior A modified c=1 matrix model with new critical behavior

1994-07-04

arxiv.org/abs/hep-th/9407014v2

Phys.Lett. B340 (1994) 35-42

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 2 figures (uuencoded postscript files), PUPT-1479

Scientific paper

10.1016/0370-2693(94)91294-7

By introducing a $\int dt \, g\left(\Tr \Phi^2(t)\right)^2$ term into the action of the $c=1$ matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical ``bubbles'' which touch one another at single points. At a special value of $g$, the sum over connected surfaces behaves as $\Delta^2 \log\Delta$, where $\Delta$ is the cosmological constant (the sum over surfaces of area $A$ goes as $A^{-3}$). For comparison, in the conventional $c=1$ model the sum over planar surfaces behaves as $\Delta^2/ \log\Delta$.

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