Superparticles, p-Form Coordinates and the BPS Condition

TL;DR

The paper addresses realizing extended supersymmetry with $p$-form charges in arbitrary dimensions by formulating a universal framework where coordinates parametrize all $p$-form brane charges. It develops a first-order action for $n$ superparticles in $(d-n,n)$ with κ-symmetry and large bosonic symmetry, and then generalizes to a universal model with spinor coordinates $(\theta^\alpha)$ and p-form coordinates $(X^{\alpha\beta})$ that yield the on-shell BPS constraint via ${\det P = 0}$. It further shows how this universal model reduces to the conventional multi-particle system and provides a detailed $(2,2)$ example to illustrate the mechanism of the BPS condition and its solutions. The work offers a path toward covariant realizations of brane charges and possible extensions to branes and M-theory, with potential applications to brane dynamics and dualities in higher dimensions.

Abstract

A model for $n$ superparticles in $(d-n,n)$ dimensions is studied. The target space supersymmetry involves a product of $n$ momentum generators, and the action has $n(n+1)/2$ local bosonic symmetries and $n$ local fermionic symmetries. The precise relation between the symmetries presented here and those existing in the literature is explained. A new model is proposed for superparticles in arbitrary dimensions where coordinates are associated with all the $p$-form charges occuring in the superalgebra. The model naturally gives rise to the BPS condition for the charges.