On Central Charges and Hamiltonians for 0-brane dynamics

TL;DR

This paper analyzes the properties of central charges and BPS conditions for 0-branes across various dimensions, revealing duality invariants and classifying BPS states with different supersymmetry fractions.

Contribution

It provides a comprehensive study of BPS conditions, duality invariants, and charge classifications for 0-branes in theories with various supersymmetries and dimensions.

Findings

Derived U-duality invariant conditions on charge spectra.

Classified BPS states preserving different fractions of supersymmetry.

Analyzed BPS mass spectrum for toroidal compactifications.

Abstract

We consider general properties of central charges of zero branes and associated duality invariants, in view of their double role, on the bulk and on the world volume (quantum-mechanical) theory. A detailed study of the BPS condition for the mass spectrum arising from toroidal compactifications is given for 1/2, 1/4 and 1/8 BPS states in any dimensions. As a byproduct, we retreive the U-duality invariant conditions on the charge (zero mode) spectrum and the orbit classification of BPS states preserving different fractions of supersymmetry. The BPS condition for 0-branes in theories with 16 supersymmetries in any dimension is also discussed.