pp-waves in 11-dimensions with extra supersymmetry
Jerome P. Gauntlett, Christopher M. Hull
TL;DR
Gauntlett and Hull analyze the Killing spinor equations for eleven dimensional pp-wave backgrounds with flux $F_4 = dx^- ∧ ξ$ and show that backgrounds preserving intermediate fractions of supersymmetry exist, notably 18, 20, 22, and 24 out of 32 (fractions 9/16, 5/8, 11/16, 3/4). The method derives the conditions on the transverse potential $H$, written as $H = sum_{ij} A_{ij} x^i x^j$ with $tr A = -1/2 ||ξ||^2$, and uses a Cartan subalgebra analysis of $SO(16)$ to identify when extra Killing spinors appear, including a spinor decomposition ε = (1 + sum x^i Ω_i) χ. They present explicit flux configurations that realize 18–24 supersymmetries, including special cases that reduce to IIA pp-waves and connections to Penrose limits of AdS × S backgrounds. The work broadens the landscape of supersymmetric M-theory backgrounds with intermediate fractions of supersymmetry and provides a framework for constructing and recognizing such solutions.
Abstract
The Killing spinor equations for pp-wave solutions of eleven dimensional supergravity are analysed and it is shown that there are solutions that preserve 18,20,22 and 24 supersymmetries, in addition to the generic solution preserving 16 supersymmetries and the Kowalski-Glikman solution preserving 32 supersymmetries.