N = 1 2 supersymmetric four-dimensional nonlinear s-models from nonanticommutative superspace (original) (raw)

Chiral models in noncommutative N=1/2 four dimensional superspace

Physical Review D, 2005

We derive the component Lagrangian for a generic N = 1/2 supersymmetric chiral model with an arbitrary number of fields in four space-time dimensions. We then investigate a toy model in which the deformation parameter modifies the undeformed potential near the origin of the field space in a way which suggests possible physical applications.

The quantum geometry of N = (2,2) non-linear σ-models

Physics Letters B, 1997

We consider a general N = (2, 2) non-linear σ-model in (2, 2) superspace. Depending on the details of the complex structures involved, an off-shell description can be given in terms of chiral, twisted chiral and semi-chiral superfields. Using superspace techniques, we derive the conditions the potential has to satisfy in order to be ultra-violet finite at one loop. We pay particular attention to the effects due to the presence of semi-chiral superfields. A complete description of N = (2, 2) strings follows from this.

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions

Russ Phys J, 1990

A new finite N = 2 supersymmetric sigma model with higher derivatives in four dimensions is formulated. The action of the model is determined in N = 2, d = 4 superspace in terms of N = 2 chiral real superfields. The Lagrangian of the theory under consideration is evaluated in N = 1 super-space and in components. By the methods of N = 2 superfield perturbation theory, it is shown that the constructed N = 2 model is ultraviolet-finite in all orders of quantum perturbation theory in 4-dimensional space-time.

Sigma models with off-shell N = (4, 4) supersymmetry and noncommuting complex structures

Journal of High Energy Physics, 2010

We describe the conditions for extra supersymmetry in N = (2, 2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4, 4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f -structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.

Geometry and duality in supersymmetric σ-models” Nucl Phys B469

Nuclear PhysicsB 469 (1996) 488-512, 1996

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson-fermion symphysis of the dual transition, and on the new geometry of the DSM. 1

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.

6D supersymmetric nonlinear sigma-models in 4D, Script N = 1 superspace

Journal of High Energy Physics, 2006

Using 4D, N = 1 superfield techniques, a discussion of the 6D sigmamodel possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.