Related papers: Three-dimensional N=4 supersymmetry in harmonic N=…

We discuss the spectrum of states of IIB supergravity on $AdS_5\times S^5$ in a manifest $SU(2,2/4)$ invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence…

New non-abelian supersymmetric generalizations of the four-dimensional Born-Infeld action are constructed in N=1 and N=2 superspace, to all orders in the gauge superfield strength. The proposed actions are dictated by simple (manifestly…

An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the…

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…

We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding…

We briefly review a class of four dimensional $\mathcal N=3$ field theories constructed by taking a quotient of $\mathcal N=4$ SYM with gauge group $U(N)$. The quotient involves a discrete symmetry that only exists for specific, order one,…

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an `existence proof' that this is indeed possible we show how to derive N=4 super Yang…

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building…

We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield…

We introduce a class of 3d theories consisting of strongly-coupled ${\mathcal N}=4$ systems coupled to ${\mathcal N}=3$ Chern-Simons gauge multiplets, which exhibit ${\mathcal N}=4$ enhancements when a peculiar condition on the Chern-Simons…

In this paper we will discuss non-anticommutative deformations of the harmonic superspace. We will analyse the non-anticommutative deformation of the superspace that break the supersymmetry from $\mathcal{N} =3$ supersymmetry to…

We analyse Feynman diagram calculational issues related to the quantum breaking of supercurrent conservation in a supersymmetric non-abelian Yang-Mills theory. For the sake of simplicity, we take a zero mass gauge field multiplet…

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 give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, $N…

A superspace formulation using superconnections and supercurvatures is specifically constructed for N=4 extended super Yang-Mills theory with a central charge in four dimensions, first proposed by Sohnius, Stelle and West long ago. We find…

This article contains an overview of some recent attempts at understanding supergravity and string duals of four dimensional gauge theories using the AdS/CFT correspondence. We discuss the general philosophy underlying the various ways to…

We survey some of the AGT relations between N=2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces.…

We consider a supersymmetric matrix quantum mechanics. This is obtained by adding Myers and mass terms to the dimensional reduction of 4d N=1 super Yang-Mills theory to one dimension. Using this model we construct 4d N=1 super Yang-Mills…

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…

We study the four-dimensional $\mathcal{N}=4$ super-Yang-Mills (SYM) theory on the unorientable spacetime manifold $\mathbb{RP}^4$. Using supersymmetric localization, we find that for a large class of local and extended SYM observables…