Quaternionic Kähler Detour Complexes and Supersymmetric Black Holes

• Published in: Communications in mathematical physics Vol. 302; no. 3; pp. 843 - 873
• Main Authors: Cherney, D., Latini, E., Waldron, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 2011
• Subjects: Classical and Quantum Gravitation; Complex Systems; Mathematical and Computational Physics; Mathematical Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Modulus Space; Black Hole; Ghost; Sigma Model; High Spin
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-010-1169-6

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional 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.