On pq-duality and explicit solutions in $c\le 1$ $2d$ gravity models

Abstract

We study the integral representation for the exact solution to nonperturbative $cle1$ string theory. A generic solution is determined by two functions $W(x)$ and $Q(x)$ which behaive at infinity like $x^p$ and $x^q$ respectively. The integral model for arbitrary $(p,q)$ models is derived which explicitely demonstrates $p-q$ duality of minimal models coupled to gravity. We discuss also the exact solutions to string equation and reduction condition and present several explicit examples.

NORDITA 93/20, FIAN-TD-04/93, latex, 20 pp

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