Abstract
We derive the $U$-duality charge orbits, as well as the related moduli spaces, of ``large'' and ``small'' extremal black holes in nonmaximal ungauged Maxwell-Einstein supergravities with symmetric scalar manifolds in $d=5$ space-time dimensions. The stabilizer groups of the various classes of orbits are obtained by determining and solving suitable $U$-invariant sets of constraints, both in ``bare'' and ``dressed'' charge bases, with various methods. After a general treatment of attractors in real special geometry (also considering nonsymmetric cases), the $\mathcal{N}=2$ ``magic'' theories, as well as the $\mathcal{N}=2$ Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal ($\mathcal{N}=4$) matter-coupled supergravity is also studied in this context.
Highlights
Five-dimensional supergravity theories with nonmaximal supersymmetry (2 N < 8), emerging from CalabiYau compactifications of M theory, admit extremal black p-brane solutions in their spectrum [1]
Spherically symmetric, and stationary solutions, the attractor mechanism [3,4,5,6] proved to be a crucial phenomenon, determining, in a universal fashion, the stabilization of scalar fields in the near-horizon geometry in terms of the fluxes of the 2-form field strengths of the Abelian vector fields coupled to the system
real special geometry (RSG) ([28,29,30,31,32,33] and references therein) is the geometry underlying the scalar manifold M5 of Abelian vector multiplets coupled to the minimal supergravity in d 1⁄4 5 space-time dimensions, namely, to N 1⁄4 2, d 1⁄4 5 theory
Summary
Five-dimensional supergravity theories with nonmaximal supersymmetry (2 N < 8), emerging from CalabiYau compactifications of M theory, admit extremal black p-brane solutions in their spectrum [1]. In particular, ungauged theories admit extremal black holes (p 1⁄4 0) and black strings (p 1⁄4 1) which are asymptotically flat and reciprocally related through U duality. These objects have been intensely studied throughout the years, due to the wide range of classical and quantum aspects they exhibit. Ungauged theories admit extremal black holes (p 1⁄4 0) and black strings (p 1⁄4 1) which are asymptotically flat and reciprocally related through U duality.. For supergravity theories with scalar manifolds which are symmetric cosets, the extremal solutions of the ungauged theory can be classified through the orbits of the relevant representation space of the U-duality group, in which the corresponding supporting charges sit. We derive the U-duality charge orbits, as well as the related moduli spaces, of ‘‘large’’ and ‘‘small’’ extremal black holes and black strings in ungauged MaxwellEinstein supergravities with symmetric scalar manifolds. We point out that all results on charge orbits can be obtained in various other ways, including the analysis of cubic norm forms of the relevant Jordan systems in d 1⁄4 5; this will be investigated elsewhere
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