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Type: Journal article
Title: Conformal superalgebras via tractor calculus
Author: Lischewski, A.
Citation: Classical and Quantum Gravity, 2015; 32(1):015020-1-015020-44
Publisher: IOP Publishing Ltd.
Issue Date: 2015
ISSN: 0264-9381
Statement of
Andree Lischewski
Abstract: We use the manifestly conformally invariant description of a Lorentzian conformal structure in terms of a parabolic Cartan geometry in order to introduce a superalgebra structure on the space of twistor spinors and normal conformal vector fields formulated in purely algebraic terms on parallel sections in tractor bundles. Via a fixed metric in the conformal class, one reproduces a conformal superalgebra structure that has been considered in the literature before. The tractor approach, however, makes clear that the failure of this object to be a Lie superalgebra in certain cases is due to purely algebraic identities on the spinor module and to special properties of the conformal holonomy representation. Moreover, it naturally generalizes to higher signatures. This yields new formulas for constructing new twistor spinors and higher order normal conformal Killing forms out of existing ones, generalizing the well-known spinorial Lie derivative. Moreover, we derive restrictions on the possible dimension of the space of twistor spinors in any metric signature.
Keywords: Conformal superalgebra; twistor spinor; tractor calculus; supersymmetry
Rights: © 2014 IOP Publishing Ltd
DOI: 10.1088/0264-9381/32/1/015020
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