Iwasawa N=8 Attractors

TL;DR

This paper explores an Iwasawa parametrization of the scalar manifold in N=8 supergravity, revealing a residual Z_4 symmetry that constrains the dyonic nature of 1/8-BPS black hole attractors.

Contribution

It introduces a new Iwasawa symplectic frame for E_7(7)/SU(8) and analyzes the resulting symmetry breaking, linking it to black hole attractor properties.

Findings

U(1) symmetry is broken to Z_4 at the scalar origin.

All 1/8-BPS attractors are non-dyonic near the scalar origin.

The symplectic frame's covariance is limited to a subgroup of SL(8,R).

Abstract

Starting from the symplectic construction of the Lie algebra e_7(7) due to Adams, we consider an Iwasawa parametrization of the coset E_7(7)/SU(8), which is the scalar manifold of N=8, d=4 supergravity. Our approach, and the manifest off-shell symmetry of the resulting symplectic frame, is determined by a non-compact Cartan subalgebra of the maximal subgroup SL(8,R) of E_7(7). In absence of gauging, we utilize the explicit expression of the Lie algebra to study the origin of E_7(7)/SU(8) as scalar configuration of a 1/8-BPS extremal black hole attractor. In such a framework, we highlight the action of a U(1) symmetry spanning the dyonic 1/8-BPS attractors. Within a suitable supersymmetry truncation allowing for the embedding of the Reissner-Nordstrom black hole, this U(1) is interpreted as nothing but the global R-symmetry of pure N=2 supergravity. Moreover, we find that the above mentioned U(1) symmetry is broken down to a discrete subgroup Z_4, implying that all 1/8-BPS Iwasawa attractors are non-dyonic near the origin of the scalar manifold. We can trace this phenomenon back to the fact that the Cartan subalgebra of SL(8,R) used in our construction endows the symplectic frame with a manifest off-shell covariance which is smaller than SL(8,R) itself. Thus, the consistence of the Adams-Iwasawa symplectic basis with the action of the U(1) symmetry gives rise to the observed Z_4 residual non-dyonic symmetry.