Abstract
We study the existence of solutions of the string equations which are pole-free on the positive real axis and exhibit such a solution following the work of Boutroux. We further study, using perturbation theory, the flows among different models and we find that there is no flow between the k=2 and k=3 theories. Moreover, we develop a nonperturbative renormalization-group scheme to extract the scaling behavior of the partition function of the k=2 model under perturbations. The key idea is to reinterpret the recent formulation, as Virasoro constraints, of the string-loop equations as generalized Callan-Symanzik renormalization-group equations.
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