dc.contributor.author Toledo, Jonathan dc.date.accessioned 2016-09-14 20:41:29 (GMT) dc.date.available 2016-09-14 20:41:29 (GMT) dc.date.issued 2016-09-14 dc.date.submitted 2016-07-15 dc.identifier.uri http://hdl.handle.net/10012/10841 dc.description.abstract This thesis is devoted to a two-pronged study of non-perturbative quantum field theory. In Part I we focus on the four-dimensional super conformal $\mathcal{N}=4$ Yang Mills theory. We compute smooth Wilson loops and correlation functions in the strong-coupling regime of the theory using the classical integrability of the dual string theory as our main tool. In both cases the solution is given as a set of integral equations of thermodynamic bethe ansatz type. The correlation function and Wilson loop are then written in terms of the corresponding TBA free energy. The equations for the Wilson loop expectation value can be used for generic smooth contours embeddable in an $\mathbb{R}^{1,1}$ subspace of $\mathbb{R}^{1,3}$. en In Part II we ask general questions about the allowed space of massive quantum field theories based only on crossing symmetry and unitarity. We approach this question in two ways. First we consider putting massive QFT into an AdS box and study the conformal boundary theory using standard conformal bootstrap tools. We call this procedure the {\it boundary bootstrap}. It is applicable in any dimension but takes its simplest form for a $1+1$ dimensional bulk QFT where we use it to obtain rigorous bounds on allowed QFT couplings. For $1+1$ dimensional QFT we are also able to obtain rigorous bounds directly in flat space using unitarity, crossing symmetry and analyticity of the S-matrix. The bounds obtained in this way agree perfectly with those obtained from the boundary bootstrap. dc.language.iso en en dc.publisher University of Waterloo en dc.subject quantum field theory en dc.subject non-perturbative quantum field theory en dc.subject N=4 super yang mills en dc.subject S-matrix bootstrap en dc.title Exact results in QFT: Minimal Areas and Maximal Couplings en dc.type Doctoral Thesis en dc.pending false uws-etd.degree.department Physics and Astronomy en uws-etd.degree.discipline Physics en uws-etd.degree.grantor University of Waterloo en uws-etd.degree Doctor of Philosophy en uws.contributor.advisor Vieira, Pedro uws.contributor.affiliation1 Faculty of Science en uws.published.city Waterloo en uws.published.country Canada en uws.published.province Ontario en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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