“Triangular” extremal dilatonic dyons

Explicit dyonic solutions in four-dimensional Einstein–Maxwell-dilaton theory are known only for three particular values of the dilaton coupling constant: a=0,1,3. However, numerical evidence was presented on existence of dyons admitting an extremal limit in theories with more general sequence of dilaton couplings a=n(n+1)/2 labeled by an integer n  . Apart from the lower members n=0,1,2n=0,1,2, this family of theories does not have motivation from supergravity/string theory, and analytical origin of the above sequence remained unclear so far. We fill the gap showing that this formula follows from analyticity of the dilaton function at the AdS2×S2AdS2×S2 event horizon of the extremal dyonic black hole, with n being the leading dilaton power in the Taylor expansion. We also derive generalization of this rule for asymptotically anti-de Sitter dyonic black holes with spherical, planar and hyperbolic topology of the horizon.