Small Black Hole Constituents and Horizontal Symmetry

TL;DR

This paper extends the classification of extremal black hole charge configurations by analyzing small single-centered constituents using horizontal symmetry, reducing the number of invariants and considering various supergravity models.

Contribution

It introduces a new analysis of small black hole constituents with horizontal symmetry, simplifying the invariant structure across different supergravity theories.

Findings

Number of invariants reduced from four to one for small constituents.

Applicable to both N=2 and N=8 supergravity models.

Provides a unified classification framework for extremal black holes.

Abstract

By exploiting the role of the horizontal symmetry SL(2,R), we extend the analysis and classification of two-centered extremal black hole charge configurations to the case of "small" single-centered constituents. These latter are seen to decrease the number of independent horizontal-invariant polynomials from four to one, depending on the rank of the charge orbit supporting each of the two centers. Within U-duality groups of type E7, both reducible and irreducible symmetric supergravity models in four space-time dimensions are considered, thus encompassing N = 2 and N = 8 theories.