M-theory on pp-waves with a holomorphic superpotential and its membrane and matrix descriptions

TL;DR

This paper introduces a new class of inhomogeneous pp-wave solutions in D=11 supergravity with 8 supersymmetries, characterized by a holomorphic superpotential, and explores their membrane and matrix theory descriptions.

Contribution

It presents novel inhomogeneous pp-wave solutions with non-constant flux and links them to supermembrane, matrix theory, and supersymmetric Yang-Mills models via a holomorphic superpotential.

Findings

New inhomogeneous pp-wave solutions with 8 supersymmetries

Superpotential determined by an arbitrary holomorphic function

Connections established with supermembrane and matrix theories

Abstract

We study a new class of inhomogeneous pp-wave solutions with 8 unbroken supersymmetries in D=11 supergravity. The 9 dimensional transverse space is Euclidean and split into 3 and 6 dimensional subspaces. The solutions have non-constant gauge flux, which are described in terms of an arbitrary holomorphic function of the complexified 6 dimensional space. The supermembrane and matrix theory descriptions are also provided and we identify the relevant supersymmetry transformation rules. The action also arises through a dimensional reduction of N=1, D=4 supersymmetric Yang-Mills theory coupled to 3 gauge adjoint and chiral multiplets, whose interactions are determined by the holomorphic function of the supergravity solution now constituting the superpotential.