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Article
From Yang–Mills in de Sitter Space to Electromagnetic Knots
We review analytic SU(2) Yang–Mills solutions with finite action on four-dimensional de Sitter space from a new perspective, by conformally map** dS \(_{4}\) to a finite Lorentzian cylinder $$(0,\pi ) \times...
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Article
Supersymmetric Calogero Models from Superfield Gauging
Using the superfield gauging procedure, we construct new \(\mathcal{N} = 2\) and \(\mathcal{N} = 4\) superfield systems that generalize Calogero models. In the bosonic limit, these systems yield rational Ca...
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Article
Pure Yang–Mills Solutions on dS4
We consider pure SU(2) Yang–Mills theory on four-dimensional de Sitter space dS4 and construct smooth and spatially homogeneous classical Yang–Mills fields. Slicing dS4 as
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Article
Action-angle variables and novel superintegrable systems
In this paper we demonstrate the effectiveness of the action-angle variables in the study of superintegrable systems. As an example, we construct the spherical and pseu-dospherical generalizations of the two-d...
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Article
Instantons and Chern-Simons flows in 6, 7 and 8 dimensions
The existence of K-instantons on a cylinder M7 = ℝτ × K/H over a homogeneous nearly Käller 6-manifold K/H requires a conformally parallel or a cocalibrated G 2-structure on M 7. Th...
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Article
New super-Calogero models and OSp(4|2) superconformal mechanics
We report on the new approach to constructing superconformal extensions of the Calogerotype systems with an arbitrary number of involved particles. It is based upon the superfield gauging of non-Abelian isomet...
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Article
New D(2, 1; α) mechanics with spin variables
We elaborate on a novel superconformal mechanics model possessing D(2, 1; α) symmetry and involving extra U(2) spin variables. It is the one-particle case of the
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Article
N = 4 mechanics, WDVV equations and polytopes
N = 4 superconformal n-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial nonlinear differential equations generalizing the Witten—Dijkgraaf—Verl...
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Article
Gauge theory in deformed \( \mathcal{N} \) = (1, 1) superspace
We review the non-anticommutative Q-deformations of \( \mathcal{N} \) = (1, 1) supersymmetric theories in four-dimens...
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Article
Open AccessA Note on Fermionic Flows of the N=(1|1) Supersymmetric Toda Lattice Hierarchy
We extend the Sato equations of the N=(1|1) supersymmetric Toda lattice hierarchy by two new infinite series of fermionic flows and demonstrate that the algebra of the flows of the extended hierarchy is the Borel...
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Article
Light-Cone Gauge for N = 2 Strings
Covariant quantization of self-dual strings in 2 + 2 flat dimensions reduces them to their zero modes, a consequence of extended world-sheet supersymmetry. We demonstrate how to arrive at the same result more ...
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Article
Open AccessHidden N = (2|2) Supersymmetry of the N = (1|1) Supersymmetric Toda Lattice Hierarchy
An N = (2|2) superfield formulation of the N = (1|1) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented.
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Article
Open AccessReal Forms of the Complex Twisted N=2 Supersymmetric Toda Chain Hierarchy in Real N=1 and Twisted N=2 Superspaces
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demonstrated that they possess a global twisted N=2 ...
