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Résumé |
String theories are generally defined through strictly perturbative, asymptotic
genus expansions, and the problem of non-perturbative completion is generically
challenging. Matrix models and their double-scaling limits to string theories
are relatively tractable in this regard, and have seen a surge of research
interest due to their connection to black hole physics and supersymmetric gauge
theory. I will present a large N description of Hermitian matrix model partition
functions, based on spectral geometry and resurgent analysis, that accounts for
all non-perturbative physics at play and is fully background independent. I will
show that resurgence requires the inclusion of both positive and negative
tension D-branes, and renders this initially asymptotic large N solution well-
defined. Analytic continuation to arbitrarily strong coupling requires
connection formulae, which we show to be given by the topological string
connection formulae of Iwaki and Mariño. These ingredients put together lead to
precise matches with finite N quantities. I will then present some early results
on extensions of this work to matrix model correlation functions. |
