M-theory PP-waves, Penrose Limits and Supernumerary Supersymmetries

TL;DR

This work analyzes broad classes of supersymmetric pp-waves in M-theory, focusing on how 16 standard Killing spinors are augmented by supernumerary ones under special flux and geometry choices. By classifying the 3-form structures into two Case1/Case2 families, the authors derive precise conditions for coordinate independence of Killing spinors, enabling consistent reductions to type IIA D0-branes or pp-waves and subsequent T-duality to type IIB backgrounds. They connect these geometric supersymmetries to exactly solvable light-cone string theories and to DLCQ matrix models, illustrating dual descriptions of M-theory sectors via D0, IIA/IIB strings, and matrix quantum mechanics. The results illuminate when worldsheet or matrix-model supersymmetries are linearly realized and how Penrose limits of AdS spacetimes feed into maximally or partially supersymmetric pp-waves with rich phenomenology for holography and gauge/gravity duality.

Abstract

We study supersymmetric pp-waves in M-theory, their dimensional reduction to D0-branes or pp-waves in type IIA, and their T-dualisation to solutions in the type IIB theory. The general class of pp-waves that we consider encompass the Penrose limits of AdS_p\times S^q with (p,q)=(4,7), (7,4), (3,3), (3,2), (2,3), (2,2), but includes also many other examples that can again lead to exactly-solvable massive strings, but which do not arise from Penrose limits. All the pp-waves in D=11 have 16 ``standard'' Killing spinors, but in certain cases one finds additional, or ``supernumerary,'' Killing spinors too. These give rise to linearly-realised supersymmetries in the string or matrix models. A focus of our investigation is on the circumstances when the Killing spinors are independent of particular coordinates (x^+ or transverse-space coordinates), since these will survive at the field-theory level in dimensional reduction or T-dualisation.