LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System

Abstract

In this paper we elaborate on the correspondence between the quantum Hall system with filling factor equal to one and the N=4 SYM theory in the 1/2 BPS sector, previously mentioned in the [hep-th/0409174, hep-th/0409115]. We show the equivalence of the two in various formulations of the quantum Hall physics. We present an extension of the noncommutative Chern-Simons Matrix theory which contains independent degrees of freedom (fields) for particles and quasiholes. The BPS configurations of our model, which is a model with explicit particle-quasihole symmetry, are in one-to-one correspondence with the 1/2 BPS states in the N=4 SYM. Within our model we shed light on some less clear aspects of the physics of the N=4 theory in the 1/2 BPS sector, like the giant dual-giant symmetry, stability of the giant gravitons, and stringy exclusion principle and possible implications of the (fractional) quantum Hall effect for the AdS/CFT correspondence.

32 pages, 4 figures; v2: A typo fixed, references added

References in corpus (30)

• Large N Field Theories, String Theory and Gravity
• Bubbling AdS space and 1/2 BPS geometries
• Invasion of the Giant Gravitons from Anti-de Sitter Space
• Giant Gravitons in Conformal Field Theory
• Large branes in AdS and their field theory dual
• A toy model for the AdS/CFT correspondence
• SUSY and Goliath
• The Quantum Hall Fluid and Non-Commutative Chern Simons Theory
• Quantum Hall states as matrix Chern-Simons theory
• Exact Correlators of Giant Gravitons from dual N=4 SYM
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Superstars and Giant Gravitons
• Tiny Graviton Matrix Theory: DLCQ of IIB Plane-Wave String Theory, A Conjecture
• On Level Quantization for the Noncommutative Chern-Simons Theory
• Fermions from Half-BPS Supergravity
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Classification of All 1/2 BPS Solutions of the Tiny Graviton Matrix Theory
• Giant Hedge-Hogs: Spikes on Giant Gravitons
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Chern-Simons Theories on Noncommutative Plane
• W-Infinity and String Theory
• A Note on Noncommutative Chern-Simons Theories
• A matrix model for a quantum hall droplet with manifest particle-hole symmetry
• Noncommutative Chern-Simons Solitons
• Towards the solution to the giant graviton puzzle
• Algebraic Aspects of the Fractional Quantum Hall Effect
• Infinite Symmetry in the Fractional Quantum Hall Effect
• $W_{\infty }$ Algebras in the Quantum Hall Effect
• Bosonization of non-relativstic fermions in 2-dimensions and collective field theory
• Self-dual Chern-Simons solitons in noncommutative space

Cited by in corpus (38)

• The Library of Babel: On the origin of gravitational thermodynamics
• Large N BPS states and emergent quantum gravity
• Anatomy of bubbling solutions
• Matrix Model Maps in AdS/CFT
• On Half-BPS States of the ABJM Theory
• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --
• Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra
• Large N Spectrum of two Matrices in a Harmonic Potential and BMN energies
• Correlators Of Operators with a Large R-charge
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• Free particles from Brauer algebras in complex matrix models
• Emergent classical spacetime from microstates of an incipient black hole
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Dynamics of Giant-Gravitons in the LLM geometry and the Fractional Quantum Hall Effect
• Tiny Graviton Matrix Theory/SYM Correspondence: Analysis of BPS States
• Stretched Horizon and Entropy of Superstars
• Fractional quantum Hall effect on the two-sphere: a matrix model proposal
• On Classification Of The Bubbling Geometries
• The giant graviton expansion in $Ad{S}_5\times S^5$
• Modular Symmetry and Fractional Charges in N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect
• Correlations vs connectivity in R-charge
• Bubbling AdS and Vacuum String Field Theory
• BPS Condensates, Matrix Models and Emergent String Theory
• Nonrelativistic Supersymmetry in Noncommutative Space
• Noncommutative Fluids
• Graph duality as an instrument of Gauge-String correspondence
• Edge excitations of the Chern Simons matrix theory for the FQHE
• Half-BPS Geometries and Thermodynamics of Free Fermions
• Quantum Mechanics of Lowest Landau Level Derived from N=4 SYM with Chemical Potential
• Target space entanglement in a matrix model for the bubbling geometry
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• On Toda Equation and Half BPS Supergravity Solution in M-Theory
• BPS R-balls in N=4 SYM on R X S^3, Quantum Hall Analogy and AdS/CFT Holography
• A Universal Behavior of Half BPS Probes in the Superstar Ensemble
• Black Hole Production from High Energy Scattering in AdS/CFT
• M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect