Related papers: Three-dimensional N=4 superconformal superfield th…
We review the non-anticommutative Q-deformations of N=(1,1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories…
One of the simplest examples of non-invertible symmetries in higher dimensions appears in 4d Maxwell theory, where its $SL(2,\mathbb{Z})$ duality group can be combined with gauging subgroups of its electric and magnetic 1-form symmetries to…
In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two ($1 + 1$)-dimensional (2D)…
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these…
We study orbifolds of ${\cal N} = 4$ U(n) super-Yang-Mills theory given by discrete subgroups of SU(2) and SU(3). We have reached many interesting observations that have graph-theoretic interpretations. For the subgroups of SU(2), we have…
We study certain new models of supersymmetric quantum mechanics. The explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonians and supercharges is given. It is shown that the Hamiltonian…
Exploiting the gauging procedure developed by us in hep-th/0605211, we study the relationships between the models of N=4 mechanics based on the off-shell multiplets (4,4,0) and (1,4,3). We make use of the off-shell N=4, d=1 harmonic…
We present a Lagrangian formulation for N=4 supersymmetric quantum-mechanical systems describing the motion in external non-Abelian self-dual gauge fields. For any such system, one can write a component supersymmetric Lagrangian by…
We investigate the non-BPS realm of 3d ${\cal N} = 4$ superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d ${\cal N} = 4$…
Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$…
We obtain by superfield methods the exceptional representations of the OSp(2N/4,R) and SU(2,2/1) superalgebras which extend to supersingletons of SU(2,2/2N) and F(4), respectively. These representations describe superconformally coupled…
We compute supersymmetric indices to test mirror symmetry of three-dimensional $\mathcal{N}=4$ gauge theories and dualities of half-BPS enriched boundary conditions and interfaces in four-dimensional $\mathcal{N}=4$ Super Yang-Mills theory.…
We discover a four-dimensional $\mathcal{N}=1$ supersymmetric field theory that is dual to the $\mathcal{N}=4$ super Yang-Mills theory with gauge group $SU(2n+1)$ for each $n$. The dual theory is constructed through the diagonal gauging of…
We construct superconformal mechanics with $N=3$ and $N=4$ supersymmetries that were inspired by analogies with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight…
We discuss some of the key topological aspects of a two $(1+1)$-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of {\it chiral} superfield formalism. We provide the…
We argue that off-shell dualities between d=1 supermultiplets with different sets of physical bosonic components and the same number of fermionic ones are related to gauging some symmetries in the actions of the supermultiplets with maximal…
We present new explicit realizations of the most general N=4, d=1 superconformal symmetry D(2,1;\alpha) in the models of N=4 superconformal mechanics based on the reducible multiplets (1,4,3)\oplus(0,4,4), (3,4,1)\oplus(0,4,4) and…
We find an infinite family of $4D$ $\mathcal{N}=2$ interacting superconformal field theories which enter the description of the strong-coupling limit of $SU(2N+1)$ gauge theories with hypermultiplets in the…
In these lecture notes we first assemble the basic ingredients of supersymmetric gauge theories (particularly N=4 super-Yang-Mills theory), supergravity, and superstring theory. Brane solutions are surveyed. The geometry and symmetries of…
We construct a new $N=4$ non-semisimple gauged supergravity in three dimensions with $E_{6(2)}/SU(6)\times SU(2)$ scalar manifold and $SO(4)\ltimes \mathbf{T}^6$ gauge group. Depending on the values of the gauge coupling constants, the…