Related papers: Vector Supersymmetry: Casimir operators and contra…
In a (0,1) supersymmetric (SUSY) six-dimensional gauge theory, a gauge fermion gives rise to box anomalies. These anomalies are completely canceled by assuming a vector multiplet of (1,1) SUSY. With a T^2/Z_3 orbifold compactification of…
In these introductory lectures, we review the theoretical tools used in constructing supersymmetric field theories and their application to physical models. We first introduce the technology of two-component spinors, which is convenient for…
We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the…
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…
The Bannai-Ito algebra $B(n)$ of rank $(n-2)$ is defined as the algebra generated by the Casimir operators arising in the $n$-fold tensor product of the $osp(1,2)$ superalgebra. The structure relations are presented and representations in…
We use superspace methods to study an SYK-like model with $\mathcal N=2$ supersymmetry in one dimension, and an analog of this model in two dimensions. We find the four-point function as an expansion in the basis of eigenfunctions of the…
Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…
We study the structure of asymptotic symmetries in N=1+1 supersymmetric extension of three-dimensional gravity with torsion. Using a natural generalization of the bosonic anti-de Sitter asymptotic conditions, we show that the asymptotic…
We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras $\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$ in…
In this paper, we define generalized Casimir operators for a loop contragredient Lie superalgebra and prove that they commute with the underlying Lie superalgebra. These operators have applications in the decomposition of tensor product…
We find the GKO coset construction of the dimension 4 Casimir operator that contains the quartic WZW currents contracted with completely symmetric SU(N) invariant tensors of ranks 4, 3, and 2. The requirements, that the operator product…
We study the representation theory of the Kazama-Suzuki coset vertex operator superalgebra associated with the pair of a complex simple Lie algebra and its Cartan subalgebra. In the case of type $A_{1}$, B.L. Feigin, A.M. Semikhatov, and…
We perform a general analysis of representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless…
A recent novel derivation of the representation of Virasoro singular vectors in terms of Jack polynomials is extended to the supersymmetric case. The resulting expression of a generic super-Virasoro singular vector is given in terms of a…
A description of the orthosymplectic Lie superalgebra $osp(2n+1/2m)$ and also of its $q-$deformed analogue $U_q[osp(2n+1/2m)]$ in terms of a new set of generators, called Green generators, is given. These generators are very different form…
An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a…
We linearize nonlinear supersymmetry in the Volkov-Akulov (VA) theory for extended SUSY in two dimensional spacetime ($d = 2$) based on the commutator algebra. Linear SUSY transformations of basic component fields for general vector…
We conjecture the connection between $su$ and $so$ members of universal, in Vogel's sense, multiplets. The key element is the notion of the {\it vertical componentwise sum} $\oplus_v$ of Young diagrams. Representations in the decomposition…
The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the…
We show that in the supersymmetry framework described by a Poincar\'{e} superalgebra with tensorial central charges the role of generalized superconformal symmetry which contains all these central charges is played by $OSp(1|2^{k})$, where…