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Fractional Quantum Hall Effect in a Relativistic Field Theory
David B Kaplan1, Srimoyee Sen2
1Institute for Nuclear Theory, Box 351550, University of Washington, Seattle, Washington 98195-1550, USA.
Abstract:
We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the fractional quantum Hall effect in the infrared, both in the continuum and on the lattice. The UV completion consists of a perturbative U(1)×U(1) gauge theory with integer-charged fields, while the low energy spectrum consists of nontrivial topological phases supporting fractional currents, bulk anyonic excitations, and exotic phenomena such as a fractional quantum spin Hall effect. We show explicitly how fractionally charged chiral edge states emerge in the IR.
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