Unification of All String Models with $c<1$

Abstract

A 1-matrix model is proposed, which nicely interpolates between double-scaling continuum limits of all multimatrix models. The interpolating partition function is always a KP $τ$-function and always obeys ${\cal L}_{-1}$-constraint and string equation. Therefore this model can be considered as a natural unification of all models of 2d-gravity (string models) with $c\leq 1.$