Poisson geometry of sigma models with extended supersymmetry (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.

Two-dimensional supersymmetric nonlinear σ-models with torsion

Physics Letters B, 1984

We present a new kind of supersymmetric nonlinear o-models in two dimensions characterized by the fact that the manifold of the scalar fields has torsion. In this way we obtain new geometries compatible with supersymmetry. IfN 2 the manifolds are hermitian rather than k~ihlerian.

The geometry of supersymmetric non-linear sigma models in D≤ 2 dimensions

2008

After a review of the two-dimensional supersymmetric non-linear sigma models and the geometric constraints they put on the target space, I focus on sigma models in one dimension. The mathematical framework in terms of supersymmetry and complex geometry will also be studied and reviewed. The geometric constraints arising in D = 1 are more general than in D = 2, and can only after some assumptions be reduced to the well known geometries arising in the two dimensional case.

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.

First-order supersymmetric sigma models and target space geometry

Journal of High Energy Physics, 2006

We study the conditions under which N = (1, 1) generalized sigma models support an extension to N = (2, 2). The enhanced supersymmetry is related to the target space complex geometry. Concentrating on a simple situation, related to Poisson sigma models we develop a language that may help us analyze more complicated models in the future. In particular, we uncover a geometrical framework which contains generalized complex geometry as a special case.

Generalized supersymmetric non-linear sigma models

Physics Letters B, 2004

We rewrite the N = (2, 2) non-linear sigma model using auxiliary spinorial superfields defining the model on T ⊕ * T , where T is the tangent bundle of the target space M. This is motivated by possible connections to Hitchin's generalized complex structures. We find the general form of the second supersymmetry compatible with the known one for the original model.

Geometry of the N = 2 supersymmetric sigma model with Euclidean worldsheet

Journal of High Energy Physics, 2009

We investigate the target space geometry of supersymmetric sigma models in two dimensions with Euclidean signature, and the conditions for N = 2 supersymmetry. For a real action, the geometry for the N = 2 model is not the generalized Kähler geometry that arises for Lorentzian signature, but is an interesting modification of this which is not a complex geometry.

Geometry and Duality in Supersymmetric sigma-Models

1996

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-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.

Geometry and duality in supersymmetric σ-models

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