On Black Hole Effective Potential in 6D/7D N=2 Supergravity

TL;DR

This paper computes the explicit quaternionic metric of the moduli space in 6D N=2 supergravity using harmonic superspace, explores its uplift to 7D, and studies black attractor potentials.

Contribution

It provides the explicit scalar field expression of the moduli space metric and analyzes black hole effective potentials in 6D/7D supergravity.

Findings

Explicit quaternionic metric for the moduli space derived.

Uplift of 6D supergravity results to 7D described.

Black attractor potential aspects analyzed.

Abstract

Using the harmonic superspace method and the duality between real and complex representations of hypermultiplets, we compute the explicit scalar field expression of the quaternionic metric $G_{mn}$ of the moduli space SO(1,1)x[SO(4,k)/(SO(4)xSO(k))] of 6D N=2 supergravity with generic k Maxwell supermultiplets. The obtained metric includes the particular case k=20 associated with 10D type IIA superstring on K3. Uplifting to 7D N=2 supergravity is described and aspects of 6D/7D black attractor effective potentials are studied.