Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonperturbative effects and nonperturbative definitions in matrix models
  and topological strings   We develop techniques to compute multi-instanton corrections to the 1/N
expansion in matrix models described by orthogonal polynomials. These
techniques are based on finding trans-series 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 Gross-Witten-Wadia (GWW) unitary matrix model. Moreover, we use Borel
resummation techniques and results from the theory of resurgent functions to
relate the formal multi-instanton series to the nonperturbative definition of
the matrix model. We study this relation in the case of the GWW model and its
double-scaling 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 trans-series 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
multi-instanton sectors of the matrix model

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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: econ