scholarly journals Real Killing spinors in neutral signature

2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
J. Gutowski ◽  
W.A. Sabra
Keyword(s):  
Killing Spinors

scholarly journals Killing superalgebras for lorentzian five-manifolds

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Andrew Beckett ◽  
José Figueroa-O’Farrill
Keyword(s):  
Spin Manifold ◽  
Field Equations ◽  
Spinor Bundle ◽  
Killing Spinors ◽  
Spinor Connection ◽  
Spencer Cohomology ◽  
Definition Of ◽  
Supersymmetric Theories ◽  
Filtered Deformations

Abstract We calculate the relevant Spencer cohomology of the minimal Poincaré superalgebra in 5 spacetime dimensions and use it to define Killing spinors via a connection on the spinor bundle of a 5-dimensional lorentzian spin manifold. We give a definition of bosonic backgrounds in terms of this data. By imposing constraints on the curvature of the spinor connection, we recover the field equations of minimal (ungauged) 5-dimensional supergravity, but also find a set of field equations for an $$ \mathfrak{sp} $$ sp (1)-valued one-form which we interpret as the bosonic data of a class of rigid supersymmetric theories on curved backgrounds. We define the Killing superalgebra of bosonic backgrounds and show that their existence is implied by the field equations. The maximally supersymmetric backgrounds are characterised and their Killing superalgebras are explicitly described as filtered deformations of the Poincaré superalgebra.

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

Killing spinors on Lorentzian manifolds

2003 ◽  
Vol 45 (3-4) ◽  
pp. 285-308 ◽  
Author(s):  
Christoph Bohle
Keyword(s):  
Lorentzian Manifolds ◽  
Killing Spinors

scholarly journals Hidden symmetries and Lie algebra structures from geometric and supergravity Killing spinors

2016 ◽  
Vol 33 (16) ◽  
pp. 165002 ◽  
Author(s):  
Özgür Açık ◽  
Ümit Ertem
Keyword(s):  
Lie Algebra ◽  
Hidden Symmetries ◽  
Killing Spinors

scholarly journals New supergravities with central charges and Killing spinors in 2+1 dimensions

1996 ◽  
Vol 467 (1-2) ◽  
pp. 183-212 ◽  
Author(s):  
P.S. Howe ◽  
J.M. Izquierdo ◽  
G. Papadopoulos ◽  
P .K. Townsend
Keyword(s):  
Killing Spinors

Spin structures and killing spinors on lens spaces

1987 ◽  
Vol 4 (3) ◽  
pp. 277-287 ◽  
Author(s):  
A. Franc
Keyword(s):  
Lens Spaces ◽  
Spin Structures ◽  
Killing Spinors

scholarly journals Stability of Riemannian manifolds with Killing spinors

2017 ◽  
Vol 28 (01) ◽  
pp. 1750005 ◽  
Author(s):  
Changliang Wang
Keyword(s):  
Riemannian Manifolds ◽  
Einstein Manifold ◽  
Stability Result ◽  
Warped Products ◽  
Einstein Manifolds ◽  
Killing Spinors ◽  
Parallel Spinors ◽  
Unstable Manifolds ◽  
The Stability ◽  
Complete Riemannian Manifolds

Riemannian manifolds with nonzero Killing spinors are Einstein manifolds. Kröncke proved that all complete Riemannian manifolds with imaginary Killing spinors are (linearly) strictly stable in [Stable and unstable Einstein warped products, preprint (2015), arXiv:1507.01782v1 ]. In this paper, we obtain a new proof for this stability result by using a Bochner-type formula in [X. Dai, X. Wang and G. Wei, On the stability of Riemannian manifold with parallel spinors, Invent. Math. 161(1) (2005) 151–176; M. Wang, Preserving parallel spinors under metric deformations, Indiana Univ. Math. J. 40 (1991) 815–844]. Moreover, existence of real Killing spinors is closely related to the Sasaki–Einstein structure. A regular Sasaki–Einstein manifold is essentially the total space of a certain principal [Formula: see text]-bundle over a Kähler–Einstein manifold. We prove that if the base space is a product of two Kähler–Einstein manifolds then the regular Sasaki–Einstein manifold is unstable. This provides us many new examples of unstable manifolds with real Killing spinors.

scholarly journals Generalized Killing spinors and Lagrangian graphs

2014 ◽  
Vol 37 ◽  
pp. 141-151 ◽  
Author(s):  
Andrei Moroianu ◽  
Uwe Semmelmann
Keyword(s):  
Killing Spinors ◽  
Generalized Killing Spinors
Sign in / Sign up

Export Citation Format

Share Document