Adams-Iwasawa N=8 Black Holes

TL;DR

This paper analyzes the geometry of the exceptional Lie group E7(7) related to N=8 supergravity, computing the Iwasawa decomposition and exploring implications for black hole attractors and symmetry breaking.

Contribution

It provides an explicit Iwasawa decomposition of E7(7) and investigates the origin of scalar manifolds and symmetry breaking in N=8 supergravity black hole solutions.

Findings

U(1) symmetry breaks to Z_4 near scalar manifold origin

Iwasawa parametrization uses a non-compact Cartan subalgebra

Results compared with other known bases

Abstract

We study some of the properties of the geometry of the exceptional Lie group E7(7), which describes the U-duality of the N=8, d=4 supergravity. In particular, based on a symplectic construction of the Lie algebra e7(7) due to Adams, we compute the Iwasawa decomposition of the symmetric space M=E7(7)/(SU(8)/Z_2), which gives the vector multiplets' scalar manifold of the corresponding supergravity theory. The explicit expression of the Lie algebra is then used to analyze the origin of M as scalar configuration of the "large" 1/8-BPS extremal black hole attractors. In this framework it turns out that the U(1) symmetry spanning such attractors is broken down to a discrete subgroup Z_4, spoiling their dyonic nature near the origin of the scalar manifold. This is a consequence of the fact that the maximal manifest off-shell symmetry of the Iwasawa parametrization is determined by a completely non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E7(7), which breaks down the maximal possible covariance SL(8,R) to a smaller SL(7,R) subgroup. These results are compared with the ones obtained in other known bases, such as the Sezgin-van Nieuwenhuizen and the Cremmer-Julia /de Wit-Nicolai frames.