Related papers: Superspace Parafermions
Auxiliary field methods in D=2 (or 3), N=2 supersymmetric (SUSY) nonlinear sigma models (NLSMs) are studied. For these models auxiliary fields as Lagrange multipliers belong to a vector or a chiral superfield, which gives a Kahler quotient…
In a previous paper, the first three authors formulated a precise conjecture about the dimension of the {\it generalized Severi variety} $M^n_{d,g; {\rm S}, {\bf k}}$ of degree-$d$ holomorphic maps $\mathbb{P}^1 \rightarrow \mathbb{P}^n$…
We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from…
We show that the large $N$ limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This…
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For…
We review non-linear sigma-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2,2) superfields. We provide evidence to support the conjecture that all N=(2,2)…
(N=2)-superspace without torsion is described, which is equivalent to an 8-space with a discrete internal subspace. A number and a character of ties determine now an internal symmetry group, while in the supersymmetrical models this one is…
We construct noncommutative versions of both the minimal and the new minimal supersymmetric Grand Unified Theories. The enveloping-algebra formalism is used to carry out such constructions. The beautiful formulation of the Higgs sector of…
This review is devoted to some aspects of non-linear Supersymmetry in four dimensions that can be efficiently described via nilpotent superfields, in both rigid and curved Superspace. Our focus is mainly on the partial breaking of rigid…
New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it…
This review is dedicated to two-dimensional sigma models with flag manifold target spaces, which are generalizations of the familiar $CP^{n-1}$ and Grassmannian models. They naturally arise in the description of continuum limits of spin…
Reductive W-algebras which are generated by bosonic fields of spin-1, a single spin-2 field and fermionic fields of spin-3/2 are classified. Three new cases are found: a `symplectic' family of superconformal algebras which are extended by…
We discuss non-Lorentzian Lagrangian field theories in $2n-1$ dimensions that admit an $SU(1,n)$ spacetime symmetry which includes a scaling transformation. These can be obtained by a conformal compactification of a $2n$-dimensional…
We give a survey of several models of irreducible complementary series representations and their limits, special representations, for the groups SU(n,1) and SO(n,1), including new ones. These groups, whose geometrical meaning is well known,…
Many qualitatively new features of WZNW models associated to noncompact cosets are due to zero modes with continuous spectrum. Insight may be gained by reducing the theory to its zero-mode sector, the mini-superspace limit. This will be…
We consider the fully constrained version of the next-to-minimal supersymmetric extension of the standard model (cNMSSM) in which a singlet Higgs superfield is added to the two doublets that are present in the minimal extension (MSSM).…
As an extension of our previous work concerning the large N reduction on group manifolds, we study the large N reduction on coset spaces. We show that large N field theories on coset spaces are described by certain corresponding matrix…
The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3.…
We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory…
$\mathcal{N}=2$ supersymmetric $Spin(n)$ gauge theory admits hypermultiplets in spinor representations of the gauge group, compatible with $\beta\leq0$, for $n\leq 14$. The theories with $\beta<0$ can be obtained as mass-deformations of the…