On Symmetries of Extremal Black Holes with One and Two Centers

TL;DR

This paper explores the symmetries and duality structures of extremal black holes with one and two centers, emphasizing the role of E7 groups and SL(2,R) in their flux and invariant polynomial structures.

Contribution

It provides a detailed analysis of the symplectic structure and duality symmetries in multi-centered extremal black hole solutions, highlighting the role of horizontal SL(2,R) symmetry.

Findings

Identification of E7 duality groups in black hole fluxes

Elucidation of SL(2,R) symmetry in two-centered solutions

Derivation of invariant polynomial relations for two-centered configurations

Abstract

After a brief introduction to the Attractor Mechanism, we review the appearance of groups of type E7 as generalized electric-magnetic duality symmetries in locally supersymmetric theories of gravity, with particular emphasis on the symplectic structure of fluxes in the background of extremal black hole solutions, with one or two centers. In the latter case, the role of an "horizontal" symmetry SL(2,R) is elucidated by presenting a set of two-centered relations governing the structure of two-centered invariant polynomials.