N=2 Superparticles, RR Fields, and Noncommutative Structures of (super)-Spacetime

Abstract

The recent developments in superstring theory prompted the study of non-commutative structures in superspace. Considering bosonic and fermionic strings in a constant antisymmetric background yields a non-vanishing commutator between the bosonic coordinates of the spacetime. Likewise, the presence of constant Ramond–Ramond (RR) background leads to a non-vanishing anti-commutator for the Grassmann coordinates of the superspace. The non-vanishing commutation relation between bosonic coordinates can also be derived using a particle moving in a magnetic background, we use superparticle to show how the non-commutative structures emerge in superspace. The derivation is original and it is shown that only a D0-brane in supergravity background reproduces the results obtained in string theory.