Touching random surfaces and Liouville gravity.

Large N matrix models modified by terms of the form g(TrΦn)2 generate random surfaces which touch at isolated points. Matrix model results indicate that, as g is increased to a special value gt, the string susceptibility exponent suddenly jumps from its conventional value γ to γ γ−1 . We study this effect in Liouville gravity and attribute it to a change of the interaction term from Oeα+φ for g < gt to Oe α − φ for g = gt (α+ and α− are the two roots of the conformal invariance condition for the Liouville dressing of a matter operator O). Thus, the new critical behavior is explained by the unconventional branch of Liouville dressing in the action.