BPS States and Automorphisms

Abstract

The purpose of the present paper is twofold. In the first part, we provide an algebraic characterization of several families of $\nu =\frac{1}{2^n}$ $n\le 5$ BPS states in M theory, at threshold and non-threshold, by an analysis of the BPS bound derived from the $\mathcal{N}=1$ D=11 SuperPoincaré algebra. We determine their BPS masses and their supersymmetry projection conditions, explicitly. In the second part, we develop an algebraic formulation to study the way BPS states transform under $GL(32,\bR)$ transformations, the group of automorphisms of the corresponding SuperPoincaré algebra. We prove that all $\nu =1/2$ non-threshold bound states are SO(32) related with $\nu =1/2$ BPS states at threshold having the same mass. We provide further examples of this phenomena for less supersymmetric $\nu =1/4,1/8$ non-threshold bound states.

16 pages, RevTex, no figures, 3 tables. Published version