supersymmetric mechanics on special Kähler manifolds (original) (raw)
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Note onN=4supersymmetric mechanics on Kähler manifolds
Physical Review D, 2001
The geometric models of N = 4 supersymmetric mechanics with (2d.2d) I C-dimensional phase space are proposed, which can be viewed as one-dimensional counterparts of two-dimensional N = 2 supersymmetric sigma-models by Alvarez-Gaumé and Freedman. The related construction of supersymmetric mechanics whose phase space is a Kähler supermanifold is considered. Also, its relation with antisymplectic geometry is discussed.
Geometry and integrability in N=8 supersymmetric mechanics
Physical Review D
We construct the N = 8 supersymmetric mechanics with potential term whose configuration space is the special Kähler manifold of rigid type and show that it can be viewed as the Kähler counterpart of N = 4 mechanics related to "curved WDVV equations". Then, we consider the special case of the supersymmetric mechanics with the non-zero potential term defined on the family of U (1)invariant one-(complex)dimensional special Kähler metrics. The bosonic parts of these systems include superintegrable deformations of perturbed two-dimensional oscillator and Coulomb systems.
Generalized Kähler Manifolds and Off-shell Supersymmetry
Communications in Mathematical Physics, 2006
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace description. We construct and explain the geometric significance of the generalized Kähler potential for any generalized Kähler manifold; this potential is the superspace Lagrangian.
N=8 non-linear supersymmetric mechanics
Physics Letters B, 2006
We construct a new two-dimensional N = 8 supersymmetric mechanics with nonlinear chiral supermultiplet. Being intrinsically nonlinear this multiplet describes 2 physical bosonic and 8 fermionic degrees of freedom. We construct the most general superfield action of the sigma-model type and propose its simplest extension by a Fayet-Iliopoulos term. The most interesting property of the constructed system is a new type of geometry in the bosonic subsector, which is different from the special Kähler one characterizing the case of the linear chiral N = 8 supermultiplet.
Generic supersymmetric hyper-Kähler sigma models in
Physics Letters B, 2007
We analyse the geometry of four-dimensional bosonic manifolds arising within the context of N = 4, D = 1 supersymmetry. We demonstrate that both cases of general hyper-Kähler manifolds, i.e. those with translation or rotational isometries, may be supersymmetrized in the same way. We start from a generic N=4 supersymmetric three-dimensional action and perform dualization of the coupling constant, initially present in the action. As a result, we end up with explicit component actions for N = 4, D = 1 nonlinear sigma-models with hyper-Kähler geometry (with both types of isometries) in the target space. In the case of hyper-Kähler geometry with translational isometry we find that the action possesses an additional hidden N = 4 supersymmetry, and therefore it is N = 8 supersymmetric one.
Homogeneous K�hler manifolds: Paving the way towards new supersymmetric sigma models
Communications in Mathematical Physics, 1986
Homogeneous Kahler manifolds give rise to a broad class of supersymmetric sigma models containing, as a rather special subclass, the more familiar supersymmetric sigma models based on Hermitian symmetric spaces. In this article, all homogeneous Kahler manifolds with semisimple symmetry group G are constructed, and are classified in terms of Dynkin diagrams. Explicit expressions for the complex structure and the Kahler structure are given in terms of the Lie algebra cj of G. It is shown that for compact G, one can always find an Einstein-Kahler structure, which is unique up to a constant multiple and for which the Kahler potential takes a simple form. * On leave of absence from Fakultat fur Physik der Universitat Freiburg, FRG 1 The term "homogeneous space" is synonymous for "coset space," and similarly, the term "Hermitian symmetric space" is synonymous for "symmetric Kahler manifold"
Generalized Kähler Geometry from Supersymmetric Sigma Models
Letters in Mathematical Physics, 2006
We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri [10] regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of Gates-Hull-Roček . When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
Hyper-K�hler metrics and supersymmetry
Commun Math Phys, 1987
We describe two constructions of hyperkahler manifolds, one based on a Legendre transform, and one on a symplectic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.
Classical and Quantum Gravity, 2007
We perform an su(2) Hamiltonian reduction in the bosonic sector of the su(2)-invariant action for two free (4, 4, 0) supermultiplets. As a result, we get the five dimensional N = 4 supersymmetric mechanics describing the motion of an isospin carrying particle interacting with a Yang monopole. We provide the Lagrangian and Hamiltonian descriptions of this system. Some possible generalizations of the action to the cases of systems with a more general bosonic action, a four-dimensional system which still includes eight fermionic components, and a variant of five-dimensional N = 4 mechanics constructed with the help of the ordinary and twisted N = 4 hypermultiplets were also considered.