Universal BPS structure of stationary supergravity solutions

Abstract : We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H* pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C > of Spin*(2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C>. The invariance of a given solution with respect to supersymmetry is determined by an algebraic Dirac equation' on the Weyl spinor |C>. We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub-NUT black holes with respect with their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H*-orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes as a Lagrangian subvariety of the variety of nilpotent elements of Lie(G). We also generalise the notion of active duality transformations to an almost action' of the three-dimensional duality group G on asymptotically flat stationary solutions.
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Submitted on : Friday, July 30, 2010 - 4:03:14 PM
Last modification on : Tuesday, January 18, 2022 - 2:26:04 PM

Citation

Guillaume Bossard, Hermann Nicolai, K. S. Stelle. Universal BPS structure of stationary supergravity solutions. Journal of High Energy Physics, Springer, 2009, 0907, pp.003. ⟨10.1088/1126-6708/2009/07/003⟩. ⟨hal-00507509⟩

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