Abstract
We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional \({{\mathcal N} = 2}\) supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generate special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston’s complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.
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Acknowledgements
A.W. would like to thank Andy Neitzke and Boris Pioline for an early collaboration on this work, as well as many absolutely invaluable discussions. We would also like to thank Fiorenzo Bastianelli, Roberto Bonezzi, Olindo Corradini, Dmitry Fuchs, Carlo Iazeolla and Albert Schwarz for useful discussions and comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Cherney, D., Latini, E. & Waldron, A. Quaternionic Kähler Detour Complexes and \({\mathcal{N} = 2}\) Supersymmetric Black Holes. Commun. Math. Phys. 302, 843–873 (2011). https://doi.org/10.1007/s00220-010-1169-6
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DOI: https://doi.org/10.1007/s00220-010-1169-6