Touching Random Surfaces and Liouville Gravity

Abstract

Large $N$ matrix models modified by terms of the form $ g(\TrΦ^n)^2$ generate random surfaces which touch at isolated points. Matrix model results indicate that, as $g$ is increased to a special value $g_t$, the string susceptibility exponent suddenly jumps from its conventional value $\gamma$ to $\frac{\gamma }{\gamma -1}$. We study this effect in Ł gravity and attribute it to a change of the interaction term from $O{e}^{{\alpha }_{+}\varphi }$ for $g<g_t$ to $O{e}^{{\alpha }_{-}\varphi }$ for $g=g_t$ (${\alpha }_{+}$ and ${\alpha }_{-}$ are the two roots of the conformal invariance condition for the Ł dressing of a matter operator $O$). Thus, the new critical behavior is explained by the unconventional branch of Ł dressing in the action.

15 pages, PUPT-1486 (last paragraph of sec. 2 revised)

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