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

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

2006-05-21

arxiv.org/abs/hep-th/0605209v1

Nucl.Phys. B749 (2006) 206-224

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, one figure

Scientific paper

10.1016/j.nuclphysb.2006.05.012

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 $% \mathbb{S}^{3}$ 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 $| j_{z}| \leq j$.

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