Orbits and Attractors for N=2 Maxwell-Einstein Supergravity Theories in Five Dimensions

TL;DR

This work shows that five-dimensional N=2 MESGTs with symmetric scalar manifolds possess two distinct attractor families for extremal black holes, corresponding to BPS and non-BPS orbits linked to Euclidean Jordan algebras of degree three. The attractor equations yield V_BPS = Z^2 and V_NBPS = 9Z^2, with entropies tied to the cubic invariant I_3; the non-BPS branch carries a nonzero central charge and a matter charge invariant under the stabilizer's maximal compact subgroup, and remains non-tachyonic at quadratic order. The analysis also clarifies the orbit structure under U-duality, including exceptional cases such as J_3^O, and highlights a duality with N=6 supergravity in the SU*(6)/USp(6) case. The paper further extends the framework to six dimensions, where attractors correspond to tensionful or tensionless strings, and discusses implications for Calabi–Yau compactifications and higher-supersymmetry relations.

Abstract

BPS and non-BPS orbits for extremal black-holes in N=2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions were classified long ago by the present authors for the case of symmetric scalar manifolds. Motivated by these results and some recent work on non-supersymmetric attractors we show that attractor equations in N=2 MESGTs in d=5 do indeed possess the distinct families of solutions with finite Bekenstein-Hawking entropy. The new non-BPS solutions have non-vanishing central charge and matter charge which is invariant under the maximal compact subgroup of the stabilizer of the non-BPS orbit. Our analysis covers all symmetric space theories G/H such that G is a symmetry of the action. These theories are in one-to-one correspondence with (Euclidean) Jordan algebras of degree three. In the particular case of N=2 MESGT with scalar manifold SU*(6)/USp(6) a duality of the two solutions with regard to N=2 and N=6 supergravity is also considered.