6D Fractional Quantum Hall Effect

Abstract

We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological field theory of abelian three-form potentials with a single derivative Chern-Simons-like action coupled to a 6D anti-chiral theory of Euclidean effective strings. We derive the fractional conductivity, and explain how continued fractions which figure prominently in the classification of 6D superconformal field theories correspond to a hierarchy of excited states. Using methods from conformal field theory we also compute the analog of the Laughlin wavefunction. Compactification of the 7D theory provides a uniform perspective on various lower-dimensional gapped systems coupled to boundary degrees of freedom. We also show that a supersymmetric version of the 7D theory embeds in M-theory, and can be decoupled from gravity. Encouraged by this, we present a conjecture in which IIB string theory is an edge mode of a 10+2-dimensional bulk topological theory, thus placing all twelve dimensions of F-theory on a physical footing.

v2: 47 pages, 5 figures, clarifications and references added

References in corpus (18)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Resummation of Massive Gravity
• Generalized Global Symmetries
• Double Field Theory
• Fractional M2-branes
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• 6d Conformal Matter
• Topological boundary conditions in abelian Chern-Simons theory
• Holography without translational symmetry
• 6D SCFTs and Phases of 5D Theories
• Holographic Action for the Self-Dual Field
• M-theory branes and their interactions
• Classification of abelian spin Chern-Simons theories
• Type II Actions from 11-Dimensional Chern-Simons Theories
• Higher (Odd) Dimensional Quantum Hall Effect and Extended Dimensional Hierarchy
• Green-Schwarz Automorphisms and 6D SCFTs
• Twelve-dimensional Effective Action and T-duality
• TASI lectures on quantum matter (with a view toward holographic duality)

Cited by in corpus (28)

• Generalized Global Symmetries of $T[M]$ Theories. I
• The Branes Behind Generalized Symmetry Operators
• Higher Symmetries of 5d Orbifold SCFTs
• Universal Features of BPS Strings in Six-dimensional SCFTs
• F-theory and Dark Energy
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Fission, Fusion, and 6D RG Flows
• Revisiting the classifications of 6d SCFTs and LSTs
• The anomaly that was not meant IIB
• 4D Gauge Theories with Conformal Matter
• On the Holographic Dual of a Topological Symmetry Operator
• IIB Explored: Reflection 7-Branes
• On de Sitter Spacetime and String Theory
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• Non-Invertible Symmetries in Supergravity
• Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons
• Qubit Construction in 6D SCFTs
• $SO(4)$ Landau Models and Matrix Geometry
• Super-Spin Chains for 6D SCFTs
• Fractional Quantum Hall Effect for Extended Objects: from Skyrmionic Membranes to Dyonic Strings
• Geometric Approach to 3D Interfaces at Strong Coupling
• $SO(5)$ Landau Model and 4D Quantum Hall Effect in The $SO(4)$ Monopole Background
• FQHE and $t{t}^{\ast }$ geometry
• Topological interfaces in Chern-Simons theory and $Ad{S}_3/CF{T}_2$
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• B-brane transport in anomalous (2,2) models and localization
• Fractional Quantum Hall States on CP2 Space
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings