Higher-$n$ triangular dilatonic black holes

Understand

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 $a = \sqrt{n (n + 1)/2}$.

• From this sequence only $n = 1,\, 2$ members were known analytically so far.
• We present two new $n = 3,\, 5$ triangular solutions for the theory with different dilaton couplings $a,\, b$ in electric and magnetic sectors in which case the quantization condition reads $a b = n (n + 1)/2$.
• These are derived via the Toda chains for $B_2$ and $G_2$ Lie algebras.