D-string fluid in conifold: II. Matrix model for D-droplets on S3and S2

Motivated by similarities between Fractional Quantum Hall (FQH) systems and aspects of topological string theory on conifold, we continue in the present paper our previous study [R. Ahl Laamara, L.B. Drissi, E.H. Saidi, D-string fluid in conifold, I: Topological gauge model, Nucl. Phys. B 743 (2006) 333-353; E.H. Saidi, Topological SL(2) gauge theory on conifold, hep-th/0601020] concerning FQH droplets on conifold. Here we focus our attention on the conifold sub-varieties S3 and S2 and study the non-commutative quantum dynamics of D1 branes wrapped on a circle. We give a matrix model proposal for FQH droplets of N point like particles on S3 and S2 with filling fraction ν=1k. We show that the ground state of droplets on S3 carries an isospin j=kN(N−1)2 and gives remarkably rise to 2j+1 droplets on S2 with Cartan-Weyl charge |jz|⩽j.