Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
Tong, Lectures on the quantum hall effect (2016), arXiv:1606.06687 [hep-th]
8 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective Chern-Simons theories, and the modes which live on the boundary. The notes are aimed at graduate students in any discipline where $\hbar=1$. A working knowledge of quantum field theory is assumed. Contents: 1. The Basics (Landau levels and Berry phase). 2. The Integer Quantum Hall Effect. 3. The Fractional Quantum Hall Effect. 4. Non-Abelian Quantum Hall States. 5. Chern-Simons Theories. 6. Edge Modes.
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Chern-Simons theory on a strip yields boundary current algebras for oppositely propagating chiral bosons whose velocities follow from a bulk-boundary consistency condition and are independent of strip width.
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
Exact two-electron solutions in strong magnetic field organize into sub-Landau levels by relative angular momentum m, defining correlation subspaces that retain center-of-mass degeneracy and enable construction of pair-based many-body trial states.
Edge reconstruction of a ν=1 quantum Hall edge into a ν=1/3 side strip doubles topological sectors to Z2×Z2 degeneracy, producing 4π Josephson periodicity with energetically decoupled Z2 states.
Non-Hermitian Berry phases in time-varying media have a quantized real part due to symmetry, giving a topological index for systems including a non-Hermitian Su-Schrieffer-Heeger model.
Taub-NUT AdS black holes yield finite Hall transport coefficients originating from frame-dragging effects in holographic calculations.
citing papers explorer
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Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
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Edge modes in Chern-Simons theory on a strip
Chern-Simons theory on a strip yields boundary current algebras for oppositely propagating chiral bosons whose velocities follow from a bulk-boundary consistency condition and are independent of strip width.
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Non-identical anyon algebras from compact-field quantum geometry
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
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Engineering of Anyons on M5-Probes via Flux Quantization
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
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Sub-Landau levels in two-dimensional electron system in magnetic field
Exact two-electron solutions in strong magnetic field organize into sub-Landau levels by relative angular momentum m, defining correlation subspaces that retain center-of-mass degeneracy and enable construction of pair-based many-body trial states.
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Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
Edge reconstruction of a ν=1 quantum Hall edge into a ν=1/3 side strip doubles topological sectors to Z2×Z2 degeneracy, producing 4π Josephson periodicity with energetically decoupled Z2 states.
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Partial Quantisation of Non-Hermitian Berry Phases in Time-Varying Media
Non-Hermitian Berry phases in time-varying media have a quantized real part due to symmetry, giving a topological index for systems including a non-Hermitian Su-Schrieffer-Heeger model.
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Hall transports from Taub-NUT AdS black holes
Taub-NUT AdS black holes yield finite Hall transport coefficients originating from frame-dragging effects in holographic calculations.