Magic supergravities,N=8and black hole composites

Abstract

We present explicit U-duality invariants for the R, C, Q, O (real, complex, quaternionic, and octonionic) magic supergravities in four and five dimensions using complex forms with a reality condition. From these invariants we derive an explicit entropy function and corresponding stabilization equations which we use to exhibit stationary multicenter 1=2 Bogomol'nyi-Prasad-Sommerfield (BPS) solutions of these N 2 d 4 theories, starting with the octonionic one with E 7 ÿ25 duality symmetry. We generalize to stationary 1=8 BPS multicenter solutions of N 8, d 4 supergravity, using the consistent truncation to the quaternionic magic N 2 supergravity. We present a general solution of non-BPS attractor equations of the STU truncation of magic models. We finish with a discussion of the BPSnon-BPS relations and attractors in N 2 versus N 5, 6, 8.

4d/5d correspondence for the black hole potential and its critical points

“…In a top down approach [26,40,43,48,49] one uses some powerful group theoretical techniques, descending from the geometric properties of moduli spaces and U-duality invariants [50,51,52,53,54], to classify the solutions to the attractor equations and their properties. For theories with a symmetric scalar manifold, these methods have led to a general classification of BPS and non-BPS attractors, as well as studies of their classical stability and entropy [26,40,43,48,49].…”

All the timelike supersymmetric solutions of all ungauged d = 4 supergravities

“…[46]. There are many partial results in the literature [37,38,39,40] including very large families of solutions obtained via N = 2 truncations of the theory [31] but the derivation of a manifestly E 7(7) -invariant family of solutions on which the conjectures concerning the E 7(7) -invariant entropy formula [41] could be explicitly checked is highly desirable. Our results provide a starting point for this derivation [42].…”

“…Other useful identities are 31 We omit the product M IJ Φ KL ab which will not be used. 32 The product V I J a V L K b gives a different identity that will not be used 33 For N = 2 we automatically have J I J = δ I J and…”

N = 2 $$ \mathcal{N}=2 $$ super-EYM coloured black holes from defective Lax matrices

“…A convenient prepotential for this model was given in ref. [36] and splits the 10 complex coordinates X Λ into a singlet under the…”