Related papers: Integrable Spin Chain in Superconformal Chern-Simo…

The Sine-Gordon theory at $\frac{\beta^{2}}{8\pi} = \frac{2}{(2n+3)},\; n= 1,2,3 \cdots $ has a higher spin generalization of the $N=2$ supersymmetry with the central terms which arises from the affine quantum group $U_{q}( \hat{s \ell}…

This paper develops a new connection between supersymmetric gauge theories and the Yangian. I show that a twisted, deformed version of the pure N=1 supersymmetric gauge theory is controlled by the Yangian, in the same way that Chern-Simons…

The dilatation generator measures the scaling dimensions of local operators in a conformal field theory. In this thesis we consider the example of maximally supersymmetric gauge theory in four dimensions and develop and extend techniques to…

The AdS/CFT correspondence provides a rich testing ground for many important topics in theoretical physics. The earliest and most striking example of the correspondence is the conjectured duality between the energy spectrum of type IIB…

We consider the $\mathcal{N}=2$ SYM theory with gauge group SU($N$) and a matter content consisting of one multiplet in the symmetric and one in the anti-symmetric representation. This conformal theory admits a large-$N$ 't Hooft expansion…

We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the…

We show that every twist of pure supersymmetric Yang-Mills theory with gauge group GL(N) can be realized as an open-string field theory in topological string theory. Our approach reinterprets twists of supersymmetric Yang-Mills theory as…

In this paper, we discuss how gauging one-form symmetries in Chern-Simons theories is implemented in an A-twisted topological open string theory. For example, the contribution from a fixed H/Z bundle on a three-manifold M, arising in a BZ…

We develop the conformal bootstrap program for six-dimensional conformal field theories with $(2,0)$ supersymmetry, focusing on the universal four-point function of stress tensor multiplets. We review the solution of the superconformal Ward…

In this thesis we discuss non-perturbative phenomena emerging in gauge and in string/supergravity theories. We compute the partition function of 5D minimal supersymmetric U(1) gauge theory with extra adjoint matter in general…

We consider the non-relativistic superconformal U(N) X U(N) Chern-Simons theory with level (k,-k) possessing fourteen supersymmetries. We obtain an exact four-point scattering amplitude of the theory to all orders in 1/N and 1/k and prove…

Recently, the one dimensional model of $N$ spins with $S=\frac{1}{2}$ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}{\pi}…

We study the two-loop dilatation operator in the noncompact SL(2) sector of QCD and supersymmetric Yang-Mills theories with N=1,2,4 supercharges. The analysis is performed for Wilson operators built from three quark/gaugino fields of the…

We study spinon excitations of the integrable spin-1 (Fateev-Zamolodchikov; FZ) chain and their relation to the hidden supersymmetry. Using the notion of the supercharges earlier introduced to the spin chains, which change the system length…

We reformulate twistor-string theory as a heterotic string based on a twisted (0,2) model. The path integral localizes on holomorphic maps, while the (0,2) moduli naturally correspond to the states of N=4 super Yang-Mills and conformal…

We probe the long-range spin chain approach to planar N=4 gauge theory at high loop order. A recently employed hyperbolic spin chain invented by Inozemtsev is suitable for the SU(2) subsector of the state space up to three loops, but ceases…

We study the four-point correlator $\langle \mathcal{O}_2 \mathcal{O}_2 \mathcal{D} \mathcal{D} \rangle$ in $\mathcal{N}=4$ super Yang-Mills theory (SYM) with $SU(N)$ gauge group, where $\mathcal{O}_2$ represents the superconformal primary…

We consider the $\mathcal{N}=4$ SYM theory with gauge group $Sp(N)$ and the $\mathcal{N}=2$ superconformal field theory consisting of four hypermultiplets in the fundamental representation and one hypermultiplet in the rank-two…

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin…

We numerically investigate the Spin Density Functional theory for superconductors (SpinSCDFT) and the approximated exchange-correlation functional, derived and presented in the preceding paper I. As a test system we employ a free electron…