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

TL;DR

This paper develops a matrix model for fractional quantum Hall droplets on conifold sub-varieties S^3 and S^2, revealing their quantum dynamics and isospin properties, inspired by topological string theory and D-brane configurations.

Contribution

It introduces a novel matrix model for FQH droplets on S^3 and S^2 within conifold geometry, connecting string theory, D-branes, and quantum Hall physics.

Findings

Ground state on S^3 has isospin j=kN(N-1)/2.

Results show 2j+1 droplets on S^2 with specific charge bounds.

Model links topological string theory with quantum Hall phenomena.

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