Related papers: The ${\cal N}=4$ Supersymmetric Linear $W_{\infty}…

We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of…

Global N=2 supersymmetry in four dimensions with a gauged central charge is formulated in superspace. To find an irreducible representation of supersymmetry for the gauge connections a set of constraints is given. Then the Bianchi…

We give a new interpretation for the super loop space that has been used to formulate supersymmetry. The fermionic coordinates in the super loop space are identified as the odd generators of the Weil algebra. Their bosonic superpartners are…

We study $\mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the 't Hooft large $N$ limit, we compute the exact $2 \to 2$ scattering amplitudes of the fundamental…

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp.…

We present exact expressions for certain integrated correlators of four superconformal primary operators in the stress tensor multiplet of $\mathcal{N}=4$ supersymmetric Yang--Mills (SYM) theory with classical gauge group, $G_N$ $= SO(2N)$,…

We develop a new superfield approach to N=4 supersymmetric mechanics based on the concept of biharmonic superspace (bi-HSS). It is an extension of the N=4,d=1 superspace by two sets of harmonic variables associated with the two SU(2)…

We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and…

We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{c} ^{N=4}$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $ b c \beta \gamma $ system and contains a…

We study N=2 supersymmetric Chern-Simons Higgs models in $(2+1)$-dimensions. As we will demonstrate, an extended supersymmetric quantum mechanics algebras underlies the fermionic zero modes quantum system and the zero modes corresponding to…

O(N) symmetric $\lambda \phi^4$ field theories describe many critical phenomena in the laboratory and in the early Universe. Given N and $D\leq 3$, the dimension of space, these models exhibit topological defect classical solutions that in…

This is a long-overdue companion paper to arXiv:1512.00073. We study the relation between $sl(3|2)$ Chern-Simons supergravity on AdS$_3$ and two-dimensional CFT's with $\mathcal{N}=2$ super-$\mathcal{W}_3$ symmetry. Specifically, we carry…

Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer function and the tau function are reformulated so as to fit into…

We study the circular Wilson loop in the symmetric representation of U(N) in $\mathcal{N} = 4$ super-Yang-Mills (SYM). In the large N limit, we computed the exponentially-suppressed corrections for strong coupling, which suggests…

We study operators in the rank-$j$ totally symmetric representation of $O(N)$ in the critical $O(N)$ model in arbitrary dimension $d$, in the limit of large $N$ and large charge $j$ with $j/N\equiv \hat{j}$ fixed. The scaling dimensions of…

In our paper~\cite{KR} we began a systematic study of representations of the universal central extension $\widehat{\Cal D}\/$ of the Lie algebra of differential operators on the circle. This study was continued in the paper~\cite{FKRW} in…

We explain how twistor theory represents the self-dual sector of four dimensional gravity in terms of the loop group of Poisson diffeomorphisms of the plane via Penrose's non-linear graviton construction. The symmetries of the self-dual…

We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of…

We study theories with W-algebra symmetries and their relation to WZNW models on (super-)groups. Correlation functions of the WZNW models are expressed in terms of correlators of CFTs with W-algebra symmetry. The symmetries of the theories…

We review a recent progress in constructing the low-energy effective action of N=4 SYM theory. This theory is formulated in terms of N=2 harmonic superfields corresponding to N=2 vector multiplet and hypermultiplet. Such a formulation…