Non-perturbative double scaling limits

Details Non-perturbative double scaling limits Non-perturbative double scaling limits

2002-02-28

arxiv.org/abs/hep-th/0202205v1

Int.J.Mod.Phys. A18 (2003) 577-592

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, one figure

Scientific paper

10.1142/S0217751X03012424

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 non-linear sigma model (path) integrals. We explain how this solves one of the most fundamental limitation of the classic approach: we automatically obtain non-perturbative definitions in non-Borel summable cases. This is exemplified on the simplest possible examples involving O(N) symmetric non-linear sigma models with N-dimensional target spaces, for which we construct (multi)critical metrics. The non-perturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path) integrals.

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