Linearly-realised Worldsheet Supersymmetry in pp-wave Background

TL;DR

This paper investigates the realization of worldsheet supersymmetries in pp-wave backgrounds, revealing that supernumerary Killing spinors produce linearly-realized supersymmetries in light-cone gauge, with implications for supergravity solutions and string actions.

Contribution

It demonstrates that only supernumerary Killing spinors lead to linearly-realized worldsheet supersymmetries in light-cone gauge, and explores their effects in physical gauge and supergravity solutions.

Findings

Supernumerary Killing spinors yield linearly-realized supersymmetries.

Standard Killing spinors correspond to non-linear symmetries.

Mass terms in light-cone gauge are gauge artefacts.

Abstract

We study the linearly-realised worldsheet supersymmetries in the ``massive'' type II light-cone actions for pp-wave backgrounds. The pp-waves have have 16+N_sup Killing spinors, comprising 16 ``standard'' Killing spinors that occur in any wave background, plus N_sup ``supernumerary'' Killing spinors (0\le N_sup \le 16) that occur only for special backgrounds. We show that only the supernumerary Killing spinors give rise to linearly-realised worldsheet supersymmetries after light-cone gauge fixing, while the 16 standard Killing spinors describe only non-linearly realised inhomogeneous symmetries. We also study the type II actions in the physical gauge, and we show that although in this case the actions are not free, there are now linearly-realised supersymmetries coming both from the standard and the supernumerary Killing spinors. In the physical gauge, there are no mass terms for any worldsheet degrees of freedom, so the masses appearing in the light-cone gauge may be viewed as gauge artefacts. We obtain type IIA and IIB supergravity solutions describing solitonic strings in pp-wave backgrounds, and show how these are related to the physical-gauge fundamental string actions. We study the supersymmetries of these solutions, and find examples with various numbers of Killing spinors, including total numbers that are odd.