FERRARI, FRANK 2012 <jats:p> Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O (N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals. </jats:p> application/pdf https://sonar.ch/global/documents/70221 eng info:eu-repo/semantics/altIdentifier/doi/10.1142/s0217751x03012424 info:eu-repo/semantics/altIdentifier/issn/0217-751X info:eu-repo/semantics/openAccess International Journal of Modern Physics A. - World Scientific Pub Co Pte Lt. - 2003, vol. 18, no. 04, p. 577-591 Nuclear and High Energy Physics Astronomy and Astrophysics Atomic and Molecular Physics, and Optics NONPERTURBATIVE DOUBLE SCALING LIMITS http://purl.org/coar/resource_type/c_6501