Supergravity, Supermembrane and M(atrix) model on PP-Waves

TL;DR

This paper explores the duality between string theory on curved pp-wave backgrounds with fluxes and dual field theories, and derives the supermembrane and Matrix model actions based on geometric properties.

Contribution

It introduces a new duality conjecture for D0-branes on curved flux backgrounds and derives the supermembrane and Matrix model actions from geometric principles.

Findings

Agreement of decoupling quantities and symmetries between theories

Large curvature when dual field theory is weakly coupled

Derivation of supermembrane and Matrix model actions from null Killing vectors

Abstract

In the first part of this paper, we study the back-reaction of large-N light cone momentum on the maximally supersymmetric anti-pp-wave background. This gives the type IIA geometry of large-N D0-branes on curved space with fluxes. By taking an appropriate decoupling limit, we conjecture a new duality between string theory on that background and dual field theory on D0-branes which we derive by calculating linear coupling terms. Agreement of decoupling quantities, SO(3) \times SO(6) isometry and Higgs branch on both theories are shown. Also we find whenever dual field theory is weakly coupled, the curvature of the geometry is large. In the second part of this paper, we derive the supermembrane action on a general pp-wave background only through the properties of null Killing vector and through this, derive the Matrix model.