Related papers: Conformal supermultiplets without superpartners
We present the mathematical framework for a unified theory based upon su(1|5). The Lie superalgebra su(1|5) has irreducible representations of dimension 32, in which the 32 fundamental fermions of one generation (leptons and quarks, of left…
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously…
This paper deals with bases in a finite-dimensional Hilbert space. Such a space can be realized as a subspace of the representation space of SU(2) corresponding to an irreducible representation of SU(2). The representation theory of SU(2)…
We study the minimal unitary representations of non-compact groups and supergroups obtained by quantization of their geometric realizations as quasi-conformal groups and supergroups. The quasi-conformal groups G leave generalized…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras $su(n,n)$. Earlier were given the main multiplets of indecomposable elementary…
We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…
Massless conformal scalar field in d=4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2,2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The…
We study the SO(4)xSU(2) invariant and N=(1,0) supersymmetry-preserving nilpotent (non-anticommutative) Moyal deformation of hypermultiplets interacting with an abelian gauge multiplet, starting from their off-shell formulation in Euclidean…
Four $\ZZ_+$-bigraded complexes with the action of the exceptional infinite-dimensional Lie superalgebra E(3,6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible…
We introduce a new kind of non-relativistic ${\cal N}{=}\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\cal N}{=}\,8$, $d{=}1$ supersymmetry. Various…
We study the lowest dimensional typical and atypical representations of SU(5/3) superalgebra as a possible unified gauge theory having a natural SU(5) subalgebra with SU(3) extra structure, which will be used to accommodate three…
We give character formulae for the positive energy unitary irreducible representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using these we also derive decompositions of long superfields as they descend to the unitarity…
For p odd, the Lie group SO_0(p+1,p+1) has a family of unitary degenerate principal series representations realized on the space of real (p+1) by (p+1) skew symmetric matrices, similar to the Stein's complementary series for SL(2n,C) or…
We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…
The superselection sectors of two classes of scalar bilocal quantum fields in D>=4 dimensions are explicitly determined by working out the constraints imposed by unitarity. The resulting classification in terms of the dual of the respective…
Using the worldline SU(2|1) superfield approach, we construct N=4 superconformally invariant actions for the d=1 multiplets (1, 4, 3) and (2, 4, 2). The SU(2|1) superfield framework automatically implies the trigonometric realization of the…
Dynamical realizations of the most general N=4 superconformal group in one dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra in some…
We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite $W$-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators)…
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir…