Super coset space geometry
A. F. Kleppe, Chris Wainwright
TL;DR
This paper reviews the geometry of super coset spaces, emphasizing how their structures derive from super Lie groups and discussing isometries and Killing supervectors relevant to supersymmetric theories.
Contribution
It provides a comprehensive review of super coset space geometry, including the inheritance of structures from super Lie groups and the definition of Killing supervectors.
Findings
Analysis of the geometric structures of super coset spaces
Discussion of isometries and Killing supervectors
Extension of Killing supervectors to non-coset spaces
Abstract
Super coset spaces play an important role in the formulation of supersymmetric theories. The aim of this paper is to review and discuss the geometry of super coset spaces with particular focus on the way the geometrical structures of the super coset space G/H are inherited from the super Lie group G. The isometries of the super coset space are discussed and a definition of Killing supervectors - the supervectors associated with infinitesimal isometries - is given that can be easily extended to spaces other than coset spaces.
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