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Lazaroiu, Calin Iuliu
기하학 수리물리 연구단
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Spinors of real type as polyforms and the generalized Killing equation

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Title
Spinors of real type as polyforms and the generalized Killing equation
Author(s)
Cortes, Vicente; Calin Lazaroiu; Shahbazi, C. S.
Publication Date
2021-12
Journal
MATHEMATISCHE ZEITSCHRIFT, v.299, no.3-4, pp.1351 - 1419
Publisher
SPRINGER HEIDELBERG
Abstract
We develop a new framework for the study of generalized Killing spinors, where every generalized Killing spinor equation, possibly with constraints, can be formulated equivalently as a system of partial differential equations for a polyform satisfying algebraic relations in the Kahler-Atiyah bundle constructed by quantizing the exterior algebra bundle of the underlying manifold. At the core of this framework lies the characterization, which we develop in detail, of the image of the spinor squaring map of an irreducible Clifford module Sigma of real type as a real algebraic variety in the Kahler-Atiyah algebra, which gives necessary and sufficient conditions for a polyform to be the square of a real spinor. We apply these results to Lorentzian four-manifolds, obtaining a new description of a real spinor on such a manifold through a certain distribution of parabolic 2-planes in its cotangent bundle. We use this result to give global characterizations of real Killing spinors on Lorentzian four-manifolds and of four-dimensional supersymmetric configurations of heterotic supergravity. In particular, we find new families of Einstein and non-Einstein four-dimensional Lorentzian metrics admitting real Killing spinors, some of which are deformations of the metric of AdS(4) space-time.
URI
https://pr.ibs.re.kr/handle/8788114/10812
DOI
10.1007/s00209-021-02726-6
ISSN
0025-5874
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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