New supersymmetric σ-models with Wess-Zumino terms (original) (raw)

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.

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.

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.

New supersymmetric σ-model duality

Journal of High Energy Physics, 2010

We study dualities in off-shell 4D N = 2 supersymmetric σ-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal σ-model is superconformal. Since N = 2 superconformal σmodels (for which target spaces are hyperkähler cones) formulated in terms of polar multiplets are naturally associated with Kähler cones (which are target spaces for N = 1 superconformal σ-models), polar-polar duality generates a transformation between different Kähler cones. In the non-superconformal case, we study implications of polar-polar duality for the σ-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkähler potential and its dual. As an application of polar-polar duality, we study self-dual models. 1 kuzenko@cyllene.uwa.edu.au 2 ulf.lindstrom@fysast.uu.se 3 unge@physics.muni.cz 8 Final comments 34 A Superconformal Killing vectors 35 B Tensor multiplet formulation for N = 2 σ-models with U(1)×U(1) symmetry 36 1 See [4, 5] for alternative approaches. General N = 2 supersymmetric σ-models in harmonic superspace and their dualities were studied in [6]

Supersymmetric σ-models and graded Lie groups

Il Nuovo Cimento A, 1981

A geometrical treatment of supersymmetric a-models of ordinary and graded manifolds in given. The action is written in terms of differential forms on superspace, by means of a modified version of the Berezin duality operation. The linear sets associated to the models are explicitly exhibited and the ((reduction , > problem is discussed. 1.-Introduction. Recently a certain amount of interest has been devoted to supersymmetric generalizations of nonlinear a-models. Important results have been obtained by the study of On and CP~ supersymmetric a-models (1) both at the classical and at the quantum level. Moreover, a general treatment of supersymmetric models on Kghler manifolds (3) has been given and supersymmetrie generalizations of principal chirul (3) and symmetric space (4) a-models have been thoroughly discussed. In all these cases the models are obtained by graduation of the two-dimensional space-time, (*) To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.

Supersymmetric Sigma Model Geometry

Symmetry, 2012

This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)kähler reduction; projective superspace; the generalized Legendre construction; generalized Kähler geometry and constructions of hyperkähler metrics on Hermitian symmetric spaces.

New supersymmetric sigma-model duality

2010

We study dualities in off-shell 4D N = 2 supersymmetric σ-models, using the projective superspace approach. These include (i) duality between the real O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that the dual of any superconformal σ-model is superconformal. Since N = 2 superconformal σmodels (for which target spaces are hyperkähler cones) formulated in terms of polar multiplets are naturally associated with Kähler cones (which are target spaces for N = 1 superconformal σ-models), polar-polar duality generates a transformation between different Kähler cones. In the non-superconformal case, we study implications of polar-polar duality for the σ-model formulation in terms of N = 1 chiral superfields. In particular, we find the relation between the original hyperkähler potential and its dual. As an application of polar-polar duality, we study self-dual models. 1 kuzenko@cyllene.uwa.edu.au 2 ulf.lindstrom@fysast.uu.se 3 unge@physics.muni.cz 8 Final comments 34 A Superconformal Killing vectors 35 B Tensor multiplet formulation for N = 2 σ-models with U(1)×U(1) symmetry 36 1 See [4, 5] for alternative approaches. General N = 2 supersymmetric σ-models in harmonic superspace and their dualities were studied in [6]