D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}

Rachid Ahl Laamara; Lalla Btissam Drissi; El Hassan Saidi

doi:10.1016/j.nuclphysb.2006.05.012

paper

D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}

arXiv:hep-th/0605209 · doi:10.1016/j.nuclphysb.2006.05.012

Abstract

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 (hep-th/0604001, hep-th/0601020) concerning FQH droplets on conifold. Here we focus our attention on the conifold sub-varieties $S^{3}$ \textbf{\}and\textbf{\} $S^{2}$ 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 $S^{3}$ \textbf{\}and\textbf{\} $S^{2}$ with filling fraction $ν = \frac{1}{k}$ . We show that the ground state of droplets on carries an isospin $j = k \frac{N ( N - 1 )}{2}$ and gives remarkably rise to $2 j + 1$ droplets on $S^{2}$ with Cartan-Weyl charge $∣ j_{z} ∣ \leq j$ .

25 pages, one figure

D-string fluid in conifold: II. Matrix model for D-droplets on S^{3} and S^{2}

Abstract

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