Supersymmetry, a Biased Review (original) (raw)

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.

A brief review of supersymmetric non-linear sigma models and generalized complex geometry

2006

This is a review of the relation between supersymmetric non-linear sigma models and target space geometry. In particular, we report on the derivation of generalized K\"ahler geometry from sigma models with additional spinorial superfields. Some of the results reviewed are: Generalized complex geometry from sigma models in the Lagrangian formulation; Coordinatization of generalized K\"ahler geometry in terms of chiral, twisted chiral and semi-chiral superfields; Generalized K\"ahler geometry from sigma models in the Hamiltonian formulation.

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.

Superspaces and supersymmetries

Communications in Mathematical Physics, 1981

A theory of graded Banach modules over a Banach-Grassmann algebra is developed and applied tod.ifferential geometry of super-manifolds. The explidtstru~ture _of superspacescarryingPoincare supersymmetryand extendedsupersymmetry, including central charges, is described.

Supersymmetry in physics: An algebraic overview

Physica D: Nonlinear Phenomena, 1985

We survey the possible uses Graded Lie Algebras (GLA) might have in physics. We first review Kac's list of simple GLA including the hyperclassical algebras. A brief, mostly numerical survey of their representation theory follows. Although all GLA can find nonrelativistic applications, only a few can be applied to relativistic situations in any dimensions. Finally, the massless representations of some of these relativistic GLA are listed.