Bhargava's Cube and Black Hole Charges

TL;DR

This paper classifies the duality orbits of black hole charges in STU string compactifications using Bhargava's cube, linking algebraic structures to physical charge configurations.

Contribution

It introduces a novel geometric approach to classify black hole charge orbits via Bhargava's cube, connecting number theory with string theory dualities.

Findings

Classification of duality orbits using Bhargava's cube

Connection between algebraic structures and physical charge configurations

Insight into symmetry groups acting on black hole charges

Abstract

Black holes in a class of string compactifications, known as STU models, carry four electric and four magnetic charges. Furthermore a duality group, given by the product of three congruence subgroups of $SL(2,\mathbb{Z})$, acts on these integer valued charges. By placing these eight charges at the eight corners of a Bhargava cube, we provide a classification of the duality orbits in these theories.