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Journal ArticleDOI
Hyperkahler Metrics and Supersymmetry
TL;DR: In this paper, two constructions of hyperkahler manifolds, one based on a Legendre transform and one on a sympletic quotient, are described, which can be described geometrically.
Journal ArticleDOI
Properties of the eleven-dimensional supermembrane theory
TL;DR: In this article, the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory is studied in detail, and semiclassically quantized the closed torodial super-brane on a spacetime (Minkowski)4 × (flat 7-torus) and review some mathematical results that are relevant for path integral quantization.
Book ChapterDOI
Geometrical Formulation of Quantum Mechanics
Abhay Ashtekar,Troy A. Schilling +1 more
TL;DR: In this paper, a geometrical formulation of the postulates of quantum mechanics is presented, which, although equivalent to the standard algebraic formulation, has a very different appearance, in particular, states are now represented by points of a symplectic manifold (which happens to have in addition a compatible Riemannian metric), observables are represented by certain real-valued functions on this space, and the Schrodinger evolution is captured by the symplectic flow generated by a Hamiltonian function.
Journal ArticleDOI
Vanishing theorems and string backgrounds
TL;DR: In this paper, various vanishing theorems for the cohomology groups of compact Hermitian manifolds for which the Bismut connection has a (restricted) holonomy contained in SU(n) and classify all such manifolds of dimension four.
Journal ArticleDOI
Locally supersymmetric D = 3 non-linear sigma models
TL;DR: In this paper, the authors studied non-linear sigma models with N local supersymmetries in three space-time dimensions and showed that all N > 2 theories are associated with Einstein spaces.