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Resurgence and the Large N Expansion

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dc.contributor.advisor Herzog, Christopher en_US
dc.contributor.author Vaz, Ricardo en_US
dc.contributor.other Department of Physics. en_US
dc.date.accessioned 2017-09-20T16:51:05Z
dc.date.available 2017-09-20T16:51:05Z
dc.date.issued 2015-12-01
dc.identifier.uri http://hdl.handle.net/11401/76734 en_US
dc.description 175 pg. en_US
dc.description.abstract In this dissertation we focus on recent developments in the study of resurgence and the large N expansion. It is a well known fact that perturbative expansions, such as the large N expansion, are divergent asymptotic series. This is a signal that there are non- perturbative effects of the form exp(-N) that also need to be considered, and our original perturbative series should be upgraded to one including powers of both 1/N and exp(-N), which is called a transseries. The machinery needed to tackle transseries was developed in the 1980s under the formalism of so-called resurgence. Using its tools we can derive a web of large-order relations showing how coefficients of the transseries, perturbative and non-perturbative, are connected to each other, and this is the origin of the term resurgence. This tells us that the perturbative part already “knows†all about the non- perturbative effects. Matrix models appear in multiple contexts in theoretical physics, and this was the arena chosen to test and understand the ideas of resurgence, particularly the matrix model with a quartic potential. We consider different phases of the quartic matrix model, with special focus on the two-cut phase, in order to test the predictions of resurgence and study their implications. In the second part of the dissertation we used our knowledge of resurgent transseries and the quartic matrix model to address a different type of question. Namely, can we make use of an expansion at large N to generate results at finite N? We did this by comparing an analytical solution of the quartic matrix model at finite N to a resummation of the transseries. Moving around in parameter space we saw how the non-perturbative sectors could go from irrelevant to absolutely crucial in order to generate the correct answer at finite N. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Theoretical physics en_US
dc.subject.other Large N, Matrix Models, Resurgence en_US
dc.title Resurgence and the Large N Expansion en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Sterman, George en_US
dc.contributor.committeemember Deshpande, Abhay en_US
dc.contributor.committeemember Rocek, Martin en_US
dc.contributor.committeemember Anderson, Michael. en_US

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