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Other version: http://stacks.iop.org/11266708/2008/i=12/a=114?key=crossref.90c6633166b032c44ac494d027bd3565
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Nonperturbative effects and nonperturbative definitions in matrix models and topological strings 

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Published in  Journal of High Energy Physics. 2008, vol. 2008, no. 12, p. 114  
Abstract  We develop techniques to compute multiinstanton corrections to the 1/N expansion in matrix models described by orthogonal polynomials. These techniques are based on finding transseries solutions, i.e. formal solutions with exponentially small corrections, to the recursion relations characterizing the free energy. We illustrate this method in the Hermitian, quartic matrix model, and we provide a detailed description of the instanton corrections in the GrossWittenWadia (GWW) unitary matrix model. Moreover, we use Borel resummation techniques and results from the theory of resurgent functions to relate the formal multiinstanton series to the nonperturbative definition of the matrix model. We study this relation in the case of the GWW model and its doublescaling limit, providing in this way a nice illustration of various mechanisms connecting the resummation of perturbative series to nonperturbative results, like the cancellation of nonperturbative ambiguities. Finally, we argue that transseries solutions are also relevant in the context of topological string theory. In particular, we point out that in topological string models with both a matrix model and a large N gauge theory description, the nonperturbative, holographic definition involves a sum over the multiinstanton sectors of the matrix model.  
Stable URL  http://archiveouverte.unige.ch/unige:11920  
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