# Are there any SUSY black holes in D > 5?

Quoting from arXiv:0801.3471

Asymptotically flat BPS black hole solutions are known only for $$d = 4,\,5$$.

and I've seen this claim very timidly suggested in a couple of other places, but I couldn't find a proof.

We could define a supersymmetric black hole as such:

• Solution to some supergravity theory
• Asymptotically Minkowski, but not Minkowski
• Has a Killing vector which is asymptotically time-like (stationary)
• Has a Killing spinor
• Regular down to horizon, including no diverging scalars (so type IIA D$$0$$ does not count)

Do they exist for $$D>5$$? Is there a proof of non-existence? Or have any counterexample been found in the last ten years?

Progress: I have managed to prove there are no SUSY black holes in $$D=6$$. The vector bilinear from a symplectic Majorana

$$V^\mu \epsilon^{AB} = \bar\eta^A \gamma^\mu \eta^B$$

is null because of a Fierz identity. Thus we have an always null Killing vector and combined with the other timelike Killing with a spatially compact Killing horizon it's enough to derive a contradiction. This is compatible with the classified 6D SUSY geometries I've found in, e.g., arXiv:hep-th/0306235.

Progress 2: it appears to me like arXiv:hep-th/0504080 provides a supersymmetric black hole in 7D. Though I still need to check whether the scalars don't diverge.

• In my naivete I thought D-branes were all black-hole-like in sugra. Is this wrong? – Ryan Thorngren Sep 23 '18 at 16:58
• p-branes with $p>0$ are only asymptotically flat in the orthogonal directions, and the D$0$ has a divergent dilaton so it's not really a regular solution of the classical sugra. – Riccardo Antonelli Sep 23 '18 at 17:03