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

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 ${\mathbb{S}}^3$\textbf{\}and\textbf{\}${\mathbb{S}}^2$ 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 ${\mathbb{S}}^3$\textbf{\}and\textbf{\}${\mathbb{S}}^2$ with filling fraction $\nu =\frac{1}{k}$. We show that the ground state of droplets on carries an isospin $j=k\frac{N(N-1)}{2}$ and gives remarkably rise to $2j+1$ droplets on ${\mathbb{S}}^2$ with Cartan-Weyl charge $|j_z|\le j$.

25 pages, one figure

References in corpus (1)

• D-string fluid in conifold: I. Topological gauge model

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