Automorphic Black Holes as Probes of Extra Dimensions

TL;DR

This paper explores how automorphic forms and Langlands' reciprocity can be used to interpret black hole entropy as a probe of extra-dimensional spacetime geometry, focusing on CHL$_N$ models.

Contribution

It links black hole entropy counting functions to automorphic forms and elliptic motives, offering a geometric perspective on spacetime structure in string compactifications.

Findings

Black hole entropy in CHL$_N$ models derived from elliptic motives

Automorphic forms determine black hole counting functions independently of supersymmetry

Provides a geometric framework connecting black holes and extra dimensions

Abstract

Recent progress in the understanding of the statistical nature of black hole entropy shows that the counting functions in certain classes of models are determined by automorphic forms of higher rank. In this paper we combine these results with Langlands' reciprocity conjecture to view black holes as probes of the geometry of spacetime. This point of view can be applied in any framework leading to automorphic forms, independently of the degree of supersymmetry of the models. In the present work we focus on the class of Chaudhuri-Hockney-Lykken compactifications defined as quotients associated to $\mathZ_N$ groups. We show that the black hole entropy of these CHL$_N$ models can be derived from elliptic motives, thereby providing the simplest possible geometric building blocks of the Siegel type entropy count.