Oscillator Construction of Spectra of PP-Wave Superalgebras in Eleven Dimensions

TL;DR

This paper explores the construction of spectra for various eleven-dimensional pp-wave superalgebras using oscillator methods, extending from the maximally supersymmetric case to many non-maximal cases, and explicitly constructing their zero-mode spectra.

Contribution

It systematically classifies and constructs zero-mode spectra for a broad class of non-maximally supersymmetric pp-wave superalgebras in eleven dimensions, extending previous oscillator realizations.

Findings

Explicit zero-mode spectra for several non-maximal pp-wave superalgebras.

Most interesting pp-wave superalgebras in eleven dimensions are covered, excluding some special cases.

Oscillator methods effectively construct spectra for these superalgebras.

Abstract

After reviewing the oscillator realization of the symmetry superalgebra of the BMN matrix model on its maximally supersymmetric plane-wave background and the construction of its zero-mode spectrum, we study a large number of non-maximally supersymmetric pp-wave algebras in eleven dimensions which are obtained by various restrictions from the maximally supersymmetric case (BMN model). We also show how to obtain their zero-mode spectra, which we explicitly construct in some chosen examples. Except for some `exotic' or degenerate special cases, we believe our study covers all possible interesting pp-wave superalgebras of this kind in eleven dimensions.