N=(4,4) Type IIA String Theory on PP-Wave Background

TL;DR

This paper studies Type IIA string theory on a ten-dimensional pp-wave background obtained by compactifying the eleven-dimensional pp-wave along an isometry. Through double dimensional reduction from the eleven-dimensional pp-wave supermembrane, the authors construct the light-cone Green-Schwarz action, which is quadratic and describes two free massive ${ m obreak{N}}=(4,4)$ worldsheet multiplets with masses $m/3$ and $m/6$ (where $m = oldsymbol{ extmu} oldsymbol{ extalpha}' p^+$). They show the background preserves $24$ Killing spinors, with $16$ kinematical supersymmetries and $8$ dynamical supersymmetries, the latter being time-independent and commuting with the worldsheet Hamiltonian. The work provides a tractable framework for analyzing D-branes and matrix string theory on pp-waves and motivates further exploration of related nontrivial backgrounds. Key results include explicit Killing spinor analysis, the quadratic light-cone action, and detailed ${ m obreak{N}}=(4,4)$ transformation rules.

Abstract

We construct IIA GS superstring action on the ten-dimensional pp-wave background, which arises as the compactification of eleven-dimensional pp-wave geometry along the isometry direction. The background geometry has 24 Killing spinors and among them, 16 components correspond to the non-linearly realized kinematical supersymmetry in the string action. The remaining eight components are linearly realized and shown to be independent of x^+ coordinate, which is identified with the world-sheet time coordinate of the string action in the light-cone gauge. The resultant dynamical N=(4,4) supersymmetry is investigated, which is shown to be consistent with the field contents of the action containing two free massive supermultiplets.