Noncommutative gauge symmetry in the fractional quantum Hall effect (in EN)
We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field$$$$ \mathcal{A} $$$$ μin such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component$$$$ \mathcal{A} $$$$ 0of the probe field is coupled to the projected density operator, the spatial components$$$$ \mathcal{A} $$$$ iare best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.
- Research Organization:
- Univ. of Chicago, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- SC0009924
- OSTI ID:
- 2576114
- Journal Information:
- Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2024; ISSN 1029-8479
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- EN
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