A pp-Wave With 26 Supercharges

TL;DR

The paper constructs and analyzes an explicit 11D pp-wave that preserves $26$ supercharges, establishing its uniqueness and proving that no 11D pp-wave can preserve $28$ or $30$ supersymmetries. It develops a detailed Killing spinor and symmetry analysis, derives the full $26$-supercharge algebra, and studies spacelike compactifications to obtain a $26$-supersymmetric Type IIA background in which D0-branes are absent from the supersymmetry algebra. It further investigates orbifolds and other compactifications, demonstrating how SUSY is reduced in controlled ways and detailing a 26-supersymmetric IIA background alongside the absence of supersymmetric D-branes. An appendix provides a $28$-supersymmetric IIB pp-wave and its algebra, highlighting the subtle landscape of near-maximal SUSY pp-waves. Altogether, the work clarifies the landscape of highly supersymmetric pp-waves, their unique structures, and the brane content implications of compactifications.

Abstract

A pp-wave solution to 11-dimensional supergravity is given with precisely 26 supercharges. Its uniqueness and the absence of 11-dimensional pp-waves which preserve (precisely) 28 or 30 supercharges is discussed. Compactification on a spacelike circle gives a IIA configuration with all 26 of the supercharges. For this compactification, D0 brane charge does not appear in the supersymmetry algebra. Indeed, the 26 supercharge IIA background does not admit any supersymmetric D-branes. In an appendix, a 28 supercharge IIB pp-wave is presented along with its supersymmetry algebra.