Heterotic plane wave matrix models and giant gluons

In this paper we define and study a matrix model describing the M-theoryplane wave background with a single Horava-Witten domain wall. In the limit ofinfinite mu, the matrix model action becomes quadratic and we can identify thematrix Hamiltonian with a regularized Hamiltonian for hemispherical membranesthat carry fermionic degrees of freedom on their boundaries. The number offermionic degrees of freedom must be sixteen; this condition arises naturallyin the framework of the matrix model. We can also prove the exact E_8 symmetryof the spectrum around the membrane vacua at infinite mu, which arises as acurrent algebra at level one just as in the heterotic string. We also find thefull E_8 gauge multiplet as well as the multiple-gluon states, carried bycollections of hemispherical membranes. Finally we discuss the dual descriptionof the hemispherical membranes in terms of spherical fivebranes immersed in thedomain wall; we identify the correct vacuum of the matrix model and make somepreliminary comparisons with the (1,0) superconformal field theory.Comment: JHEP3 LaTeX, 1+42 pages, 23 EPS figures. References added, minor typos correcte