Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory

TL;DR

This work identifies and analyzes M-theory backgrounds with homogeneous fluxes on Cahen–Wallach Lorentzian symmetric spaces, revealing that generic Hpp-waves preserve 16 supersymmetries while two special points—Minkowski space and Kowalski–Glikman (KG) spacetime—preserve 32. By computing Killing spinors, isometries, and the full symmetry superalgebra, the authors uncover a rich structure, including a 38-dimensional bosonic symmetry algebra for KG and a distinct KG superalgebra. They extend these geometries to brane configurations via U-duality and Kaluza–Klein reductions, yielding H-branes, HD-branes, HNS-branes, and HF-branes with homogeneous fluxes, and analyze their supersymmetry properties. The results illuminate the landscape of maximally and partially supersymmetric backgrounds in M-theory, link homogeneous flux geometries to brane physics, and suggest avenues for solvable string theory models in these highly symmetric settings.

Abstract

We find M-theory solutions with homogeneous fluxes for which the spacetime is a lorentzian symmetric space. We show that generic solutions preserve sixteen supersymmetries and that there are two special points in their moduli space of parameters which preserve all thirty-two supersymmetries. We calculate the symmetry superalgebra of all these solutions. We then construct various M-theory and string theory branes with homogeneous fluxes and we also find new homogeneous flux-brane solutions.