Higher-n triangular dilatonic black holes

Dilaton gravity with the form fields is known to possess dyon solutions with two horizons for the discrete "triangular" values of the dilaton coupling constant $a=\sqrt{n(n+1)/2}$. This sequence first obtained numerically and then explained analytically as consequence of the regularity of the dilaton, should have some higher-dimensional and/or group theoretical origin. Meanwhile, this origin was explained earlier only for $n=1,2$ in which cases the solutions were known analytically. We extend this explanation to $n=3,5$ presenting analytical triangular solutions for the theory with different dilaton couplings $a,b$ in electric and magnetic sectors in which case the quantization condition reads $ab=n(n+1)/2$. The solutions are derived via the Toda chains for $B_2$ and $G_2$ Lie algebras. They are found in the closed form in general D space–time dimensions. Solutions satisfy the entropy product rules indicating on the microscopic origin of their entropy and have negative binding energy in the extremal case.