Related papers: Exact Three-Point Functions in $\mathcal{N}=2$ Sup…
In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we…
A problem of the hidden ${\cal N}=2$ supersymmetry deformation for next-to-leading terms in the effective action for ${\cal N}=4$ SYM theory is discussed. Using formulation of the theory in ${\cal N}=2$ harmonic superspace and exploring the…
Large $N$ melonic theories are characterized by two-point function Feynman diagrams built exclusively out of melons. This leads to conformal invariance at strong coupling, four-point function diagrams that are exclusively ladders, and…
We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of…
We study correlation functions in the one-dimensional $\mathcal{N}=2$ supersymmetric SYK model. The leading order 4-point correlation functions are computed by summing over ladder diagrams expanded in a suitable basis of conformal…
We study the instanton effective action in deformed four-dimensional N=2 and N=4 super Yang-Mills (SYM) theories. These deformed gauge theories are defined on the D-brane world-volume in the presence of constant, self-dual Ramond-Ramond…
We study the large charge sector of the defect CFT defined by the half-BPS Wilson loop in planar $\mathcal{N}=4$ supersymmetric Yang-Mills theory. Specifically, we consider correlation functions of two large charge insertions and several…
This dissertation reviews various aspects of the N=4 supersymmetric Yang--Mills theory in particular in relation with the AdS/CFT correspondence. The first two chapters are introductory. The first one contains a description of the general…
We derive an integral expression for the leading-order type I-I-I three-point functions in the $\mathfrak{su}(2) $-sector of $\mathcal{N}=4$ super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the…
We consider the $\mathcal{N}=2$ quiver gauge theory arising from a $\mathbb{Z}_M$ orbifold of $\mathcal{N}=4$ Super Yang-Mills theory. Over the years, exploiting supersymmetric localization, exact expressions for several observables have…
We study four-point correlation functions of degenerated fields in the $NS$ sector in Super-Liouville field theory. We find integral expressions for these functions using the BPZ equation, and study some superconformal properties of these…
We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even…
We consider two four-dimensional gauge theories with gauge group $SU(N)$: the $\mathcal{N}=4$ Super Yang-Mills (SYM) theory and the $\mathcal{N}=2$ quiver gauge theory obtained as a $\mathbb{Z}_2$ orbifold of $\mathcal{N}=4$ SYM. In this…
We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation…
We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general…
Correlation functions of gauge-invariant composite operators in N=4 super Yang-Mills theory can be computed by integrability using triangulations. The elementary tile in this process is the hexagon, which should be glued by appropriately…
We prove a novel action of the (three-dimensional) Heisenberg algebra on the equivariant K-theory of the Hilbert scheme of points on C2. These operators are defined via pushforwards and pullbacks via the Nakajima correspondences while…
We study correlation functions of local operators and Wilson loop expectation values in the planar limit of a 4d $\mathcal{N}=2$ superconformal ${\rm SU}(N)$ YM theory with hypermultiplets in the symmetric and antisymmetric representations…
We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…
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…