Abstract
We review the topological structure, sitting in any supergravity theory, which has been recently discovered in [7]. We describe how such a structure allows for a cohomological reformulation of the generalized Killing spinor equations which characterize bosonic supergravity solutions with unbroken supersymmetry.
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Notes
- 1.
See [8] for an extensive overview.
- 2.
- 3.
We will refer to Majorana spinors for simplicity. The discussion can be extended, when N is even, to Dirac spinors.
- 4.
We will denote with \(\gamma ^\mu \) the vectorial bilinear (2) and with \(\varGamma ^a\) the Dirac matrices.
- 5.
The author has been informed that this same equation is currently under investigation in a slightly different context [9].
- 6.
Barred spinors are defined in the usual way: \(\bar{\zeta }\equiv \zeta ^\dagger \, \varGamma _0\).
- 7.
In Euclidean signature and with the space-time topology of the sphere \(S^2\).
References
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Acknowledgements
I am particularly grateful to C. Imbimbo for a long collaboration on this subject over the years. I also thank J. Bae and J. Winding for discussions and collaboration. I finally thank V. Dobrev and all the organizers of the “X. International Symposium QUANTUM THEORY AND SYMMETRIES” for the invitation to this very interesting workshop.
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Rosa, D. (2018). The Cohomological Structure of Generalized Killing Spinor Equations. In: Dobrev, V. (eds) Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2. LT-XII/QTS-X 2017. Springer Proceedings in Mathematics & Statistics, vol 255. Springer, Singapore. https://doi.org/10.1007/978-981-13-2179-5_18
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DOI: https://doi.org/10.1007/978-981-13-2179-5_18
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