The effective Maxwell-Chern-Simons theory for FQH excitations admits a non-perturbative unitary SDiff-equivariant construction that is nevertheless non-differentiable.
Topological orders and Edge excitations in FQH states
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abstract
Fractional quantum Hall (FQH) liquids contain extremely rich internal structures which represent a whole new kind of ordering. We discuss characterization and classification of the new orders (which is called topological orders). We also discuss the edge excitations in FQH liquids, which form the so-called chiral Luttinger liquids. The chiral Luttinger liquids at the edges also have very rich structures as a reflection of the rich topological orders in the bulk. Thus, edge excitations provide us a practical way to measure topological orders in experiments.
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The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
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Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations
The effective Maxwell-Chern-Simons theory for FQH excitations admits a non-perturbative unitary SDiff-equivariant construction that is nevertheless non-differentiable.
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A superintegrable quantum field theory
The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.
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Candidate Gaugings of Categorical Continuous Symmetry
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.