We give a brief account of two recent applications of the harmonic superspace method: (i) an off-shell description of torsionful (4, 4) supersymmetric 2D sigma models in the framework of SU(2) × SU(2) harmonic superspace and (ii) the harmonic superspace formulation of “small” N = 4 SU(2) superconformal algebra and the related super KdV hierarchy.

We study the supersymmetric extension of the gauged O(3) sigma model in 2+1 dimensions and find the supersymmetry algebra. We also discuss soliton solutions in case the Maxwell term is replaced by the Born-Infeld term. We show that by appropriate choice of the potential, the self-dual equations in the Born-Infeld case coincide with those of the Maxwell’s case.

The affine Hecke algebra of type A has two parameters q,t and acts on polynomials in N variables. There are important pairwise commuting sets elements the algebra: Cherednik operators Jucys–Murphy whose simultaneous eigenfunctions nonsymmetric Macdonald polynomials, basis vectors irreducible modules algebra, respectively. For certain parameter values, it is possible for special to be with equal...

Fermionic extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. In addition, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to algeb...

Motivated by the recent analysis of the E10 sigma model for the study of M theory, we study a one-dimensional sigma model associated with the hyperbolic Kac-Moody algebra G2 and its link to D = 5, N = 2 pure supergravity, which closely resembles in many ways D = 11 supergravity. The bosonic equations of motion and the Bianchi identity for D = 5 pure supergravity match the equations of the level...

For each unital $C^*$-algebra $A$, we denote $cel_{CU}(A)=\sup\{cel(u):u\in CU(A)\}$, where $cel(u)$ is the exponential length of $u$ and $CU(A)$ closure commutator subgroup $U_0(A)$. In this paper, prove that $cel_{CU}(A)=2\pi$ provided $A$ an $AH$ algebras with slow dimension growth whose real rank not zero. On other hand, $cel_{CU}(A)\leq 2\pi$ when algebra ideal property no (if further assu...

We calculate the S-matrix in the gauge-fixed sigma-model on AdS 5 × S 5 to the leading order in perturbation theory, and analyze how supersymmetry is realized on the scattering states. A mild nonlocality of the supercharges implies that their action on multi-particle states does not follow the Leibniz rule, which is replaced by a nontrivial coproduct. The plane wave symmetry algebra is thus nat...