Related papers: Structure Constants in $\mathcal{N} = 4$ SYM and S…
In this thesis, we study the integrands of a special four-point correlation function formed of protected half-BPS operators and scattering amplitudes in planar supersymmetric $\mathcal{N}=4$ Yang-Mills. We use the `soft-collinear bootstrap'…
Form factors in planar $\mathcal{N}=4$ super-Yang-Mills theory have a dual description in terms of periodic Wilson loops. This duality maps the multi-collinear expansion of the former to an operator product expansion of the latter. The…
Three-point functions of analytic (chiral primary) operators in N=4 Yang-Mills theory in four dimensions are calculated using the harmonic superspace formulation of this theory. In the case of the energy-momentum tensor multiplet anomaly…
We consider correlation functions of supersymmetrized determinant operators in self-dual super Yang-Mills (SYM). These provide a generating function for correlators of arbitrary single-trace half-BPS operators, including, for appropriate…
We report on a systematic study of scalar field three-point functions in planar SU(N) N=4 super Yang-Mills theory. The motivation for this work is to provide sufficient data for future conjectures on the higher-loop form of the structure…
Basso, Komatsu and Vieira recently proposed an all-loop framework for the computation of three-point functions of single-trace operators of ${\cal N}=4$ super-Yang-Mills, the "hexagon program". This proposal results in several remarkable…
We study three-point functions of operators on the $1/2$ BPS Wilson loop in planar $\mathcal{N}=4$ super Yang-Mills theory. The operators we consider are "defect changing operators", which change the scalar coupled to the Wilson loop. We…
We review the results for the Sudakov form factor in N=4 super Yang-Mills theory up to the three-loop level. At each loop order, the form factor is expressed as a linear combination of only a handful scalar integrals, with small integer…
We incorporate gauge-invariant local composite operators into the twistor-space formulation of $\mathcal{N}=4$ Super Yang-Mills theory. In this formulation, the interactions of the elementary fields are reorganized into infinitely many…
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use…
We discuss recent progress in the determination of correlators of chiral primary operators in N=4 Super-Yang-Mills theory, based on a combination of superconformal covariance arguments in N=2 harmonic superspace, and Intriligator's…
We use Integrability techniques to compute structure constants in N=4 SYM to leading order. Three closed spin chains, which represent the single trace gauge-invariant operators in N=4 SYM, are cut into six open chains which are then sewed…
Planar N=4 supersymmetric Yang-Mills theory appears to be perturbatively integrable. This work reviews integrability in terms of a Yangian algebra and compares the application to the problems of anomalous dimensions and scattering…
Planar maximally supersymmetric Yang-Mills theory (N=4 SYM) is a special quantum field theory. A few of its remarkable features are conformal symmetry at the quantum level, evidence of integrability and, moreover, it is a prime example of…
We bootstrap the three-point form factor of the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known…
We propose an integrability setup for the computation of correlation functions of gauge-invariant operators in $\mathcal{N}=4$ supersymmetric Yang-Mills theory at higher orders in the large $N_{\text{c}}$ genus expansion and at any order in…
We consider four-point functions of protected, double- and single-trace operators in the large central charge limit. We use superconformal symmetry to disentangle the contribution of protected operators in the partial wave decomposition.…
We study three-point correlation functions of local operators in planar $\mathcal{N}=4$ SYM at weak coupling using integrability. We consider correlation functions involving two scalar BPS operators and an operator with spin, in the so…
The partition function of four dimensional Euclidean, non-supersymmetric SU(2) Yang--Mills theory is calculated in the perturbative and weak coupling regime i.e. in a small open ball about the flat connection (what we call the vicinity of…
We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field…