higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
synthetic differential geometry
Introductions
from point-set topology to differentiable manifolds
geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry
Differentials
Tangency
The magic algebraic facts
Theorems
Axiomatics
Models
differential equations, variational calculus
Chern-Weil theory, ∞-Chern-Weil theory
Cartan geometry (super, higher)
The notion of super Klein geometry is essentially that of homogeneous space (coset space) in the context of supergeometry. It is the supergeometric counterpart of Klein geometry.
Super Klein geometries form the local models for super Cartan geometries.
super Minkowski spacetimes are quotients of super Poincare groups by spin groups
similarly super anti de Sitter spacetimes are super cosets, this plays a central role in the AdS-CFT correspondence:
super anti de Sitter spacetime | |
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4 | |
5 | |
7 |
The supersphere is the super coset space .
The supersphere is the super coset space of orthosymplectic groups (GJS 18).
A. F. Kleppe, Chris Wainwright, Super coset space geometry, (arXiv:hep-th/0610039)
A. F. Schunck, Chris Wainwright, A geometric approach to scalar field theories on the supersphere, (arXiv:hep-th/0409257)
Constantin Candu, Vladimir Mitev, Volker Schomerus, Spectra of Coset Sigma Models, (arXiv:1308.5981)
Etienne Granet, Jesper Lykke Jacobsen, Hubert Saleur, Spontaneous symmetry breaking in 2D supersphere sigma models and applications to intersecting loop soups, (arXiv:1810.07807)
Last revised on April 30, 2019 at 09:43:16. See the history of this page for a list of all contributions to it.