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Abstract We present SU(2|1) supersymmetric mechanics on n-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV equations specified by the manifold’s metric and curvature tensor. We consider the most general u(2)-valued prepotential, which contains...

AbstractSU(2|1) supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an \( \mathcal{N}=4 \) supersymmetrization of the quantum U(2) spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra \( \widehat{su}\left(2\Big|1\right) \). The full...

The rational Calogero model based on an arbitrary rank-n Coxeter root system is spherically reduced to a superintegrable angular model of a particle moving on S n−1 subject to a very particular potential singular at the reflection hyperplanes. It is outlined how to find conserved charges and to construct intertwining operators. We deform these models in a \( \mathcal{P}\mathcal{T...

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in \( {\mathbb{R}}^3 \) under the influence of a quartic potential. Then we describe...

Recent years have seen an upsurge of interest in dynamical realizations of the superconformal group SU(1, 1|2) in mechanics. Remarking that SU(1, 1|2) is a particular member of a chain of supergroups SU(1, 1|n) parametrized by an integer n, here we begin a systematic study of SU(1, 1|n) multi-particle mechanics. A representation of the superconformal algebra su(1, 1|n) is...

We introduce a new kind of non-relativistic \( \mathcal{N} \) = 8 supersymmetric mechanics, associated with worldline realizations of the supergroup SU(2|2) treated as a deformation of flat \( \mathcal{N} \) = 8, d=1 supersymmetry. Various worldline SU(2|2) superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed...

We present the minimal realization of the ℓ-conformal Galilei group in 2+1 dimensions on a single complex field. The simplest Lagrangians yield the complex PaisUhlenbeck oscillator equations. We introduce a minimal deformation of the ℓ = 1/2 conformal Galilei (a.k.a. Schrödinger) algebra and construct the corresponding invariant actions. Based on a new realization of the d = 1...

The spherical reduction of the rational Calogero model (of type A n−1 and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n−2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a...

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical...

The coset Sp(2, ℝ)/U(1) is parametrized by two real scalar fields. We generalize the formalism of auxiliary tensor (bispinor) fields in U(1) self-dual nonlinear models of abelian gauge fields to the case of Sp(2, ℝ) self-duality. In this new formulation, Sp(2, ℝ) duality of the nonlinear scalar-gauge equations of motion is equivalent to an Sp(2, ℝ) invariance of the auxiliary...

It is long known that the rational Calogero model describing n identical particles on a line with inverse-square mutual interaction potential is quantum superintegrable. We review the (nonlinear) algebra of the conserved quantum charges and the intertwiners which relate the Liouville charges at couplings g and g±1. For integer values of g, these intertwiners give rise to...

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kähler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kähler 6-manifolds are prominent...

We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold X 6 in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order α′ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a...