"Triangular" extremal dilatonic dyons

TL;DR

This paper analytically derives the quantization rule for extremal dilatonic dyons in Einstein-Maxwell-dilaton theory, explaining the discrete sequence of dilaton couplings and extending results to various horizon topologies.

Contribution

It provides the first analytical derivation of the dilaton coupling quantization rule based on horizon analyticity and generalizes extremal dyon solutions to different horizon geometries.

Findings

Quantization rule for dilaton coupling constants derived analytically.

Existence of extremal dyons confirmed for a discrete sequence of couplings.

Generalization to black holes with various horizon topologies.

Abstract

Explicit dyonic dilaton black holes of the four-dimensional Einstein-Maxwell-dilaton theory are known only for two particular values of the dilaton coupling constant $a =1,\sqrt{3}$, while for other $a$ numerical evidence was presented earlier about existence of extremal dyons in theories with the discrete sequence of dilaton couplings $a=\sqrt{n(n+1)/2}$ with integer $n$. Apart from the lower members $n=1,\,2$, this family of theories does not have motivation from supersymmetry or higher dimensions, and so far the above quantization rule has not been derived analytically. We fill this gap showing that this rule follows from analyticity of the dilaton at the $AdS_2\times S^2$ event horizon with $n$ being the leading dilaton power in the series expansion. We also present generalization for asymptotically anti-de Sitter dyonic black holes with spherical, plane and hyperbolic topology of the horizon.