Related papers: Hypermultiplets and hypercomplex geometry from 6 t…
N=2 conformal supergravity in five dimensions is constructed via a systematic off-shell reduction scheme from maximal conformal supergravity in six dimensions which is (2,0). The dimensional reduction of the (2,0) Weyl multiplet in six…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
We construct a dilaton Weyl multiplet for $N = 3$ conformal supergravity in four dimensions. We couple an on-shell vector multiplet to the standard Weyl multiplet and use the field equations of the vector multiplet to replace some of the…
This is an exposition of some recent results on ECS manifolds, by which we mean pseudo-Riemannian manifolds of dimensions greater than 3 that are neither conformally flat nor locally symmetric, and have parallel Weyl tensor. All ECS metrics…
We show that the (1,0) tensor and hypermultiplet supersymmetry variations can be uplifted to loop space. Upon dimensional reduction we make contact with abelian five-dimensional super Yang-Mills, which has a nonabelian generalization that…
Our aim is to derive the effective action in four dimensions resulting by reducing dimensionally the ten-dimensional ${\cal N}=1$ heterotic supergravity coupled to ${\cal N}=1$ super Yang-Mills over manifolds admitting a nearly-K\"{a}hler…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
Recent works have demonstrated reasonable success of representation learning in hypercomplex space. Specifically, "fully-connected layers with Quaternions" (4D hypercomplex numbers), which replace real-valued matrix multiplications in…
We consider the master fields for HS multiplets defined on 10-dimensional tensorial extension \tilde{\cal M} of D=4 space-time described as a coset \tilde{\cal M}={\cal M}/Sl(2;C) of 16-parameter Maxwell group {\cal M}. The tensorial…
Five-dimensional gauge and gravity theories are known to exhibit striking properties. D=5 is the lowest dimension where massive tensor states appear naturally, providing a testing ground for perturbative insights into six-dimensional tensor…
In this paper we study the birational geometry of HyperKaehler manifolds by combining the method of minimal model program and the traditional approach of symplectic geometry.
In this article, we study a generalisation of the Seiberg-Witten equations, replacing the spinor representation with a hyperKahler manifold equipped with certain symmetries. Central to this is the construction of a (non-linear) Dirac…
This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice…
Tensoring two on-shell super Yang-Mills multiplets in dimensions $D\leq 10$ yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) $\mathbb{D}$ with each…
We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas…
The universal hypermultiplet moduli space metric in the type-IIA superstring theory compactified on a Calabi-Yau threefold is related to integrable systems. The instanton corrections in four dimensions arise due to multiple wrapping of BPS…
We propose the definition of (twisted) generalized hyperkaehler geometry and its relation to supersymmetric non-linear sigma models. We also construct the corresponding twistor space.
Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an $\mathcal{N}=(4,0)$ multiplet has a four…
Relying on the method of spinorial geometry, purely bosonic supersymmetric solutions in N=2, five-dimensional supergravity theories coupled to vector multiplets in all space-time signatures are found. Explicit examples of some new solutions…
We discuss various aspects of moment map geometry in symplectic and hyperK\"ahler geometry. In particular, we classify complete hyperK\"ahler manifolds of dimension $4n$ with a tri-Hamiltonian action of a torus of dimension $n$, without any…