Embedding Fractional Quantum Hall Solitons in M-theory Compactifications
A. Belhaj, N-E. Fahssi, E.H. Saidi, A. Segui
TL;DR
This paper constructs models of fractional quantum Hall states using M-theory compactifications, linking string theory, geometry, and condensed matter phenomena, and reproduces known experimental filling factors.
Contribution
It introduces a novel M-theory based framework for modeling fractional quantum Hall states via hyper-Kähler manifolds and D-brane configurations.
Findings
Reproduces Laughlin, Haldane, and Jain filling factors
Connects M-theory compactifications with quantum Hall physics
Provides geometric interpretation of fractional states
Abstract
We engineer U(1)^n Chern-Simons type theories describing fractional quantum Hall solitons (QHS) in 1+2 dimensions from M-theory compactified on eight dimensional hyper-K\"{a}hler manifolds as target space of N=4 sigma model. Based on M-theory/Type IIA duality, the systems can be modeled by considering D6-branes wrapping intersecting Hirzebruch surfaces F_0's arranged as ADE Dynkin Diagrams and interacting with higher dimensional R-R gauge fields. In the case of finite Dynkin quivers, we recover well known values of the filling factor observed experimentally including Laughlin, Haldane and Jain series.
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