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=root 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, 2in 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, bin 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 Dspace-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. (c) 2018 The Authors. Published by Elsevier B.V.