An N=8 supersymmetric mechanics with potential is built on rigid special Kähler manifolds, yielding bosonic Hamiltonians that include superintegrable deformations of the 2D oscillator and Coulomb problem.
Lectures on Special Kahler Geometry and Electric--Magnetic Duality Rotations
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abstract
In these lectures I review the general structure of electric--magnetic duality rotations in every even space--time dimension. In four dimensions, which is my main concern, I discuss the general issue of symplectic covariance and how it relates to the typical geometric structures involved by N=2 supersymmetry, namely Special K\"ahler geometry for the vector multiplets and either HyperK\"ahler or Quaternionic geometry for the hypermultiplets. I discuss classical continuous dualities versus non--perturbative discrete dualities. How the moduli space geometry of an auxiliary dynamical Riemann surface (or Calabi--Yau threefold) relates to exact space--time dualities is exemplified in detail for the Seiberg Witten model of an $SU(2)$ gauge theory.
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Geometry and integrability in $\mathcal{N}=8$ supersymmetric mechanics
An N=8 supersymmetric mechanics with potential is built on rigid special Kähler manifolds, yielding bosonic Hamiltonians that include superintegrable deformations of the 2D oscillator and Coulomb problem.