Note onN=4supersymmetric mechanics on Kähler manifolds (original) (raw)

Kähler geometry and SUSY mechanics

Nuclear Physics B - Proceedings Supplements, 2001

We present two examples of SUSY mechanics related with Kähler geometry. The first system is the N = 4 supersymmetric one-dimensional sigma-model proposed in hep-th/0101065. Another system is the N = 2 SUSY mechanics whose phase space is the external algebra of an arbitrary Kähler manifold. The relation of these models with antisymplectic geometry is discussed.

Generalized Kähler geometry in (2, 1) superspace

Journal of High Energy Physics, 2012

Two-dimensional (2, 2) supersymmetric nonlinear sigma models can be described in (2, 2), (2, 1) or (1, 1) superspaces. Each description emphasizes different aspects of generalized Kähler geometry. We investigate the reduction from (2, 2) to (2, 1) superspace. This has some interesting nontrivial features arising from the elimination of nondynamical fields. We compare quantization in the different superspace formulations.

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.

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.

Generic N=4 supersymmetric hyper-Kähler sigma models in D=1

2006

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.

New extended superconformal sigma models and quaternion Kähler manifolds

Journal of High Energy Physics, 2009

Quaternion Kähler manifolds are known to be the target spaces for matter hypermultiplets coupled to N = 2 supergravity. It is also known that there is a oneto-one correspondence between 4n-dimensional quaternion Kähler manifolds and those 4(n + 1)-dimensional hyperkähler spaces which are the target spaces for rigid superconformal hypermultiplets (such spaces are called hyperkähler cones). In this paper we present a projective-superspace construction to generate a hyperkähler cone M 4(n+1) H of dimension 4(n + 1) from a 2n-dimensional real analytic Kähler-Hodge manifold M 2n K . The latter emerges as a maximal Kähler submanifold of the 4n-dimensional quaternion Kähler space M 4n Q such that its Swann bundle coincides with M 4(n+1) H . Our approach should be useful for the explicit construction of new quaternion Kähler metrics. The results obtained are also of interest, e.g., in the context of supergravity reduction N = 2 → N = 1, or alternatively from the point of view of embedding N = 1 matter-coupled supergravity into an N = 2 theory.

Generalized Kahler geometry and manifest N=(2,2) supersymmetric nonlinear sigma-models

Journal of High Energy Physics

Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N = (2, 2) nonlinear sigma-models. The most direct relation is obtained at the N = (1, 1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N = (2, 2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kähler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.

The geometry of supersymmetric sigma-models

We review non-linear σ-models with (2,1) and (2,2) supersymmetry. We focus on off-shell closure of the supersymmetry algebra and give a complete list of (2, 2) superfields. We provide evidence to support the conjecture that all N = (2, 2) non-linear σ-models can be described by these fields. This in its turn leads to interesting consequences about the geometry of the target manifolds. One immediate corollary of this conjecture is the existence of a potential for hyper-Kähler manifolds, different from the Kähler potential, which does not only allow for the computation of the metric, but of the three fundamental twoforms as well. Several examples are provided: WZW models on SU (2) × U (1) and SU (2) × SU (2) and four-dimensional special hyper-Kähler manifolds.