Supermanifolds - Application to Supersymmetry

Abstract

Parity is ubiquitous, but not always identified as a simplifying tool for computations. Using parity, having in mind the example of the bosonic/fermionic Fock space, and the framework of Z_2-graded (super) algebra, we clarify relationships between the different definitions of supermanifolds proposed by various people. In addition, we work with four complexes allowing an invariant definition of divergence: - an ascending complex of forms, and a descending complex of densities on real variables - an ascending complex of forms, and descending complex of densities on Grass mann variables. This study is a step towards an invariant definition of integrals of superfunctions defined on supermanifolds leading to an extension to infinite dimensions. An application is given to a construction of supersymmetric Fock spaces.

to appear in the "Michael Marinov Memorial Volume"

Cited by in corpus (8)

• Binary nonlinearization of the super AKNS system
• Drinfeld-Twisted Supersymmetry and Non-Anticommutative Superspace
• Binary Nonlinearization of the Super Akns System Under an Implicit Symmetry Constraint
• The Topological B-Model on Fattened Complex Manifolds and Subsectors of N=4 Self-Dual Yang-Mills Theory
• Invariant solutions of the supersymmetric sine-Gordon equation
• Special Holonomy and Two-Dimensional Supersymmetric Sigma-Models
• Berezin integration over anticommuting variables and cyclic cohomology
• The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems