Related papers: A Computer Algorithm For Engineering Off-Shell Mul…
In the study of supersymmetry in one dimension, various works enumerate sets of generators of garden algebras $GR(d,N)$ (and equivalently, valise Adinkras) for special cases $N = d = 4$ and $N = d = 8$, using group-theoretic methods and…
Four-dimensional N = 2 superconformal quantum field theories contain a subsector carrying the structure of a chiral algebra. Using localization techniques, we show for the free hypermultiplet that this structure can be accessed directly…
We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted…
Unfolded equations of motion for N = 1, D = 4 scalar supermultiplet are presented. We show how the superspace formulation emerges from the unfolded formulation. To analyze supersymmetric unfolded equations we extend the \sigma_-cohomology…
We provide a tensor calculus for $n$-number of ${\mathcal N}=(1,0)$ linear multiplets in six dimensions. The coupling of linear multiplets is encoded in a function ${\mathcal F}_{IJ}$ that is subject to certain constraints. We provide…
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its…
A U(2,2|4)-invariant A-model constructed from fermionic superfields has recently been proposed as a sigma model for the superstring on AdS_5xS^5. After explaining the relation of this A-model with the pure spinor formalism, the A-model…
In this note we study worldsheet two- and four-point functions at the one-loop level for the type IIA superstring in AdS(3) x S(3) x M(4) . We first address the regularization ambiguity that appears in the dispersion relation derived from…
The term `hypermachine' denotes any data processing device (theoretical or that can be implemented) capable of carrying out tasks that cannot be performed by a Turing machine. We present a possible quantum algorithm for a classically…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
We elaborate on four different types of twisted ${\cal N}=(4,4)$ supermultiplets in the $SU(2) \times SU(2)$, 2D harmonic superspace. In the conventional ${\cal N}=(4,4)$, 2D superspace they are described by the superfields $\hat q^{i a}$,…
We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear…
In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the…
We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their…
Adinkras are combinatorial objects developed to study supersymmetry representations. Gates et al. introduced the "gadget" as a function of pairs of adinkras, obtaining some mysterious results for $(n=4, k=1)$ adinkras with computer-aided…
We propose an explicit mathematical construction and plausibility arguments for how spacetime chirality and Lorentz generators emerge for minimal, off-shell 4D, $\cal N$ = 1 supermultiplets by use of a 4.4.4.4 tesselation of Riemann…
Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for…
Non-linear sigma models with extended supersymmetry have constrained target space geometries, and can serve as effective tools for investigating and constructing new geometries. Analyzing the geometrical and topological properties of sigma…
Using the harmonic superspace approach, we construct the three-dimensional N=4 supersymmetric quantum mechanics of the supermultiplet (3,4,1) coupled to an external SU(2) gauge field. The off-shell N=4 supersymmetry requires the gauge field…
In this paper we propose a quiver model of matrix quantum mechanics with 8 supercharges which, on a Higgs branch, deconstructs the worldsheet of Matrix String Theory. This discrete model evades the fermion doubling problem and, in the…