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=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 B2 and G2 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.