2 research outputs found
On Gauge Invariance of Noncommutative Chern-Simons Theories
Motivated by possible applications to condensed matter systems, in this paper
we construct U(N) noncommutative Chern-Simons (NCCS) action for a disc and for
a double-layer geometry, respectively. In both cases, gauge invariance severely
constrains the form of the NCCS action. In the first case, it is necessary to
introduce a group-valued boson field with a non-local chiral boundary action,
whose gauge variation cancels that of the bulk action. In the second case, the
coefficient matrix in the double U(N) NCCS action is restricted to be of
the form with all the matrix elements being the same integer . We suggest
that this double NCCS theory with U(1) gauge group describes the so-called
Halperin state in a double-layer quantum Hall system. Possible physical
consequences are addressed.Comment: 19 pages, 2 figures, revised versio
One-loop Shift in Noncommutative Chern-Simons Coupling
In this paper we study the one-loop shift in the coupling constant in a
noncommutative pure U(N) Chern-Simons gauge theory in three dimensions. The
one-loop shift is shown to be a constant proportional to , independent of
noncommutativity parameters, and non-vanishing for U(1) theory. Possible
physical and mathematical implications of this result are discussed.Comment: 19 pages, 2 figures, RevTex, notice added,NPB final versio