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Mtheoretic matrix models 

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Published in  Journal of High Energy Physics. 2015, vol. 1502, p. 115157  
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Open Access  SCOAP3 

Abstract  Some matrix models admit, on top of the usual ’t Hooft expansion, an Mtheorylike expansion, i.e. an expansion at large N but where the rest of the parameters are fixed, instead of scaling with N . These models, which we call Mtheoretic matrix models, appear in the localization of ChernSimonsmatter theories, and also in twodimensional statistical physics. Generically, their partition function receives nonperturbative corrections which are not captured by the ’t Hooft expansion. In this paper, we discuss general aspects of these type of matrix integrals and we analyze in detail two different examples. The first one is the matrix model computing the partition function of N = 4 $$ \mathcal{N}=4 $$ supersymmetric YangMills theory in three dimensions with one adjoint hypermultiplet and N f fundamentals, which has a conjectured Mtheory dual, and which we call the N f matrix model. The second one, which we call the polymer matrix model, computes form factors of the 2d Ising model and is related to the physics of 2d polymers. In both cases we determine their exact planar limit. In the N f matrix model, the planar free energy reproduces the expected behavior of the Mtheory dual. We also study their Mtheory expansion by using Fermi gas techniques, and we find nonperturbative corrections to the ’t Hooft expansion.  
Keywords  ChernSimons Theories — Nonperturbative Effects — 1/N Expansion — AdSCFT Correspondence  
Identifiers  arXiv: 1403.4276  
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Citation (ISO format)  GRASSI, Alba, MARINO BEIRAS, Marcos. Mtheoretic matrix models. In: Journal of High Energy Physics, 2015, vol. 1502, p. 115157. https://archiveouverte.unige.ch/unige:55735 