Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-04-29
Nucl.Phys.B750:265-288,2006
Physics
High Energy Physics
High Energy Physics - Theory
29 pages ; typos corrected, two references added
Scientific paper
10.1016/j.nuclphysb.2006.05.030
We discuss the bosonization of nonrelativistic fermions interacting with non-Abelian gauge fields in the lowest Landau level in the framework of higher dimensional quantum Hall effect. The bosonic action is a one-dimensional matrix action, which can also be written as a noncommutative field theory, invariant under $W_N$ transformations. The requirement that the usual gauge transformation should be realized as a $W_N$ transformation provides an analog of a Seiberg-Witten map, which allows us to express the action purely in terms of bosonic fields. The semiclassical limit of this, describing the gauge interactions of a higher dimensional, non-Abelian quantum Hall droplet, produces a bulk Chern-Simons type term whose anomaly is exactly cancelled by a boundary term given in terms of a gauged Wess-Zumino-Witten action.
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