Black hole attractors and pure spinors

Abstract

We construct black hole attractor solutions for a wide class of N = 2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kähler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to f k = Im (CΦ), where Φ is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Φ = Ω and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.

Towards reduction of type II theories on SU(3) structure manifolds

“…Since the ungauged 4 dimensional N = 2 action does not exhibit a potential term, all constant values for the scalar fields are a solution to the 4d equation of motion, and by construction lift to solutions of the higher dimensional theory. While no proof of this lifting property for arbitrary solutions exists to our knowledge, it does hold for certain other prominent solutions such as N = 2 black holes [7].…”

Black Hole Attractors in Extended Supergravity

“…This can be easily realized by noticing that the stabilizers of the charge orbits are non-compact, so that g Q Q BP S = Q BP S , ∀g Q ∈ E 6(2) ; g Q Q non−BP S = Q non−BP S , ∀g Q ∈ E 6(6) , (22) and thus at the critical points (recall Eq. (13))…”

Lectures on attractors and black holes

“…It is worth mentioning that the formula (6.18) has an (SU (1, 1) × SO (n))-invariant generalization given by 20) where here Λ ranging 1, ..., n, with the scalar product · defined by δ ΛΣ , the n-dim. Euclidean metric.…”

“…20 We assume the absence of more than one basin of attraction in the radial dynamics of the dilaton in the considered extremal dilaton BH supported by electric and magnetic charges constrained by p · q = 0 [81,92].…”