Touching random surfaces and Liouville gravity

Igor R. Klebanov
1995 Physical Review D, Particles and fields  
Large $N$ matrix models modified by terms of the form $ g(\Tr\Phi^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 ${\gamma\over\gamma-1}$. We study this effect in \L\ gravity and attribute it to a change of the interaction term from $O e^{\alpha_+ \phi}$ for $g<g_t$ to $O e^{\alpha_- \phi}$ for $g=g_t$
more » ... or $g=g_t$ ($\alpha_+$ and $\alpha_-$ are the two roots of the conformal invariance condition for the \L\ dressing of a matter operator $O$). Thus, the new critical behavior is explained by the unconventional branch of \L\ dressing in the action.
doi:10.1103/physrevd.51.1836 pmid:10018650 fatcat:n7cx3l75fbcztfrhr7x3maomhe