Constructing Exact Correlators In N=4 SYM Using Integrability
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Date
2019-08-09
Authors
Coronado, Frank
Journal Title
Journal ISSN
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Publisher
University of Waterloo
Abstract
This thesis is devoted to the study of correlation functions in N = 4 superconformal Yang-
Mills theory. We focus on a class of four point functions for which we achieve formal
results at finite coupling and explicit results at all-loops at weak coupling and strong
coupling in the planar ‘t Hooft limit. We use three approaches to construct them. The
first is the conformal OPE expansion for which we work out the necessary conformal
data, scaling dimensions and structure constants, using integrability. The second uses a
geometric decomposition of the four-punctured worldsheet into hexagonal patches. This
renders the four-point function as a form factor series expansion and again thanks to
integrability, the components of this series are completely worked out. In the third approach
we adopt a bootstrap philosophy, we fix completely a non-trivial four-point function at all
loops by assuming it satisfies certain properties which we learned from the weak coupling
limit of our previous two approaches. We study the strong coupling limit in our second
approach and obtain results that take the expected form for a holographic CFT dual to
classical strings in AdS. Finally we compute non-planar corrections in a double scaling
limit and manage to perform explicit all-genus resummations in special cases
Description
Keywords
conformal field theory, gauge theory, integrability, large N limit, finite coupling