Related papers: Fractional Supersymmetry As a Matrix Model
We study the relation between a supermatrix model and the free 4D, N=1 supersymmetric field theory of a massless supermultiplet with spins (3, 5/2). In order to do this, we construct a superfield formulation of the theory. We show that…
We investigate three classes of supersymmetric models which can be obtained by breaking the chiral SU(2k+3) gauge theories with one antisymmetric tensor and 2k-1 antifundamentals. For N=3, the chiral SU(2k)$\times$SU(3)$\times$U(1) theories…
In this paper, we present the quadratic associative symmetry algebra of the 3D nondegenerate maximally quantum superintegrable system. This is the complete symmetry algebra of the system. It is demonstrated that the symmetry algebra…
The algebra of multi-species anyons characterized by different statistical parameters $\nu_{ij}=e_{i}e_{j}\Phi_{i}\Phi_{j}/(2\pi)$, $i,j=1,...,n$ is redefined by basing on fermions and $k_{i}$-fermions ($k_{i}\in\bf{N}\rm /\{0,1\}$ with…
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in…
In this paper, we explore supersymmetric and 2d analogs of the SYK model. We begin by working out a basis of (super)conformal eigenfunctions appropriate for expanding a four-point function. We use this to clarify some details of the 1d…
The $K=4$ fractional superstring Fock space is constructed in terms of $\bZ_4$ parafermions and free bosons. The bosonization of the $\bZ_4$ parafermion theory and the generalized commutation relations satisfied by the modes of various…
We consider, at the linearized level, the superspace formulation of lower-dimensional F-theory. In particular, we describe the embedding of 3D Type II supergravity of the superstring, or 4D, N=1 supergravity of M-theory, into the…
We discuss a 1+2 dimensional model with unconventional supersymmetry at the boundary of an AdS${}_4$, \,$\mathcal{N}$-extended supergravity. The resulting features of the supersymmetric boundary open the possibility of describing the…
The nonlinear $n$-supersymmetry with holomorphic supercharges is investigated for the 2D system describing the motion of a charged spin-1/2 particle in an external magnetic field. The universal algebraic structure underlying the holomorphic…
In this paper we construct the supersymmetric tensor hierarchy of N=1, d=4 supergravity. We find some differences with the general bosonic construction of 4-dimensional gauged supergravities. The global symmetry group of N=1,d=4…
In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories. We classify all possible models without derivative terms in the auxiliary field of the fermionic sector and find that scalar field…
Crossing symmetry provides a powerful tool to access the non-perturbative dynamics of conformal and superconformal field theories. Here we develop the mathematical formalism that allows to construct the crossing equations for arbitrary…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
In QCD one can change the representation of the gauge group for quarks and/or the gauge group itself. Examples of such generalizations are: (a) supersymmetric Yang-Mills theory with gauge group SU(2) or SU(3); (b) QCD with SU(2) colour and…
We introduce a class of four dimensional field theories constructed by quotienting ordinary $\mathcal{N}=4$ $U(N)$ SYM by particular combinations of R-symmetry and $SL(2,\mathbb{Z})$ automorphisms. These theories appear naturally on the…
We consider ways in which conventional supersymmetry can be embedded in the set of more general fermionic transformations proposed recently [\Ref{B}] as a framework in which to study $d=10$ super Yang-Mills. Solutions are exhibited which…
We point out that some questions in quantum field theory are undecidable in a precise mathematical sense. More concretely, it will be demonstrated that there is no algorithm answering whether a given 2d supersymmetric Lagrangian theory…
The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…