BPS States and Automorphisms

TL;DR

This paper characterizes various BPS states in M theory algebraically, determines their properties, and explores how they transform under automorphisms, revealing relations among states with different supersymmetry fractions.

Contribution

It provides an algebraic classification of BPS states in M theory and analyzes their transformations under automorphisms, establishing relations between bound states with different supersymmetry fractions.

Findings

Algebraic characterization of BPS states at various fractions of supersymmetry.

Demonstration that certain non-threshold bound states are related by SO(32) automorphisms.

Explicit determination of BPS masses and projection conditions.

Abstract

The purpose of the present paper is twofold. In the first part, we provide an algebraic characterization of several families of $\nu= \frac{1}{2^n}$ $n\leq 5$ BPS states in M theory, at threshold and non-threshold, by an analysis of the BPS bound derived from the ${\cal N}=1$ D=11 SuperPoincar\'e 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 SuperPoincar\'e 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.