The Stringy Quantum Hall Fluid

Abstract

Using branes in massive Type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by D-particles, the background magnetic field corresponds to a RR 2-form flux, and the two-dimensional fluid is described by non-commutative D2-branes. The filling fraction is given by the ratio of the number of D2-branes and the number of D8-branes, and therefore by the ratio rank/level of the Chern-Simons gauge theory. Quasiparticles and quasiholes are realized as endpoints of fundamental strings on the D2-branes, and are found to possess fractional D-particle charges and fractional statistics.

24 pages, 2 figures; references added

References in corpus (7)

• Noncommutative Field Theory
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• An Exact Solution to Seiberg-Witten Equation of Noncommutative Gauge Theory
• How Noncommutative Gauge Theories Couple to Gravity
• Chern-Simons matrix model: coherent states and relation to Laughlin wavefunctions
• Realizing the Quantum Hall System in String Theory
• Seiberg-Witten Transforms of Noncommutative Solitons

Cited by in corpus (23)

• Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
• Quantum Hall Effect in a Holographic Model
• Gravity Dual of a Quantum Hall Plateau Transition
• Quantum Hall Effect in AdS/CFT
• Magnetic Backgrounds and Noncommutative Field Theory
• AC Transport at Holographic Quantum Hall Transitions
• Realizing the Quantum Hall System in String Theory
• Fluctuations and instabilities of a holographic metal
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• NC Branes and Hierarchies in Quantum Hall Fluids
• Black Holes in AdS/BCFT and Fluid/Gravity Correspondence
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Filling up complex spectral regions through non-Hermitian disordered chains
• Flowing to $\mathcal{N}=3$ Chern--Simons-matter theory
• Algebraic Geometry Realization of Quantum Hall Soliton
• Engineering of Quantum Hall Effect from Type IIA String Theory on The K3 Surface
• Quantum aspects of Seiberg-Witten map in noncommutative Chern-Simons theory
• Measurement of the H/A -> tau tau cross section and possible constraints on tan beta
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
• On Gauge Invariance of Noncommutative Chern-Simons Theories
• On the quantum equivalence of commutative and noncommutative Chern-Simons theories at higher orders
• Brane Realizations of Quantum Hall Solitons and Kac-Moody Lie Algebras
• Matrix Effective Theories of the Fractional Quantum Hall effect