منابع مشابه
Supersymmetry and Supergeometry
Dissertantenkolloquium at the university of Vienna on 29 November 2007. Some references are given, without attemtping to be complete or correct. 1. On the title and the motivation The title of this talk consists of a mathematical part and of a physical part. Supergeometry is mathematical and originated from the works of Berezin, Leites, Kostant (see e.g. in [1, 2, 3, 4]) and many others from 19...
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Motivated by Zirnbauer [Zir 1996], we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the Lie theoretical viewpoint are introduced, e.g. geodesics, isometry groups and invariant metrics on Lie supergroups and homogeneous superspaces.
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These notes are based on a series of lectures given by the first author at the school of ‘Poisson 2010’, held at IMPA, Rio de Janeiro. They contain an exposition of the theory of superand graded manifolds, cohomological vector fields, graded symplectic structures, reduction and the AKSZ-formalism.
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We analyze S equivariant cohomology from the supergeometrical point of view. For this purpose we equip the external algebra of given manifold with equivariant even super(pre)symplectic structure, and show, that its Poincare-Cartan invariant defines equivariant Euler classes of surfaces. This allows to derive localization formulae by use of superanalog of Stockes theorem.
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We present a complete solution of the WZW model on the supergroup GL(1|1). Our analysis begins with a careful study of its minisuperspace limit (“harmonic analysis on the supergroup”). Its spectrum is shown to contain indecomposable representations. This is interpreted as a geometric signal for the appearance of logarithms in the correlators of the full field theory. We then discuss the represe...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2005
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2005.v2005.n1.a1