In:
International Journal of Modern Physics A, World Scientific Pub Co Pte Ltd, Vol. 18, No. 14 ( 2003-06-10), p. 2477-2500
Abstract:
For the noncommutative torus [Formula: see text], in the case of the noncommutative parameter [Formula: see text] , we construct the basis of Hilbert space ℋ n in terms of θ functions of the positions z i of n solitons. The wrapping around the torus generates the algebra [Formula: see text], which is the Z n × Z n Heisenberg group on θ functions. We find the generators g of a local elliptic su (n), which transform covariantly by the global gauge transformation of [Formula: see text]. By acting on ℋ n we establish the isomorphism of [Formula: see text] and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero–Moser models to give the dynamics. The moment map of this twisted cotangent [Formula: see text] bundle is matched to the D-equation with the Fayet–Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det |L(u) - k| = 0 describes the brane configuration, with the dynamical variables z i of the noncommutative solitons as the moduli T ⊗ n /S n . Furthermore, in the noncommutative Chern–Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative [Formula: see text] cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.
Type of Medium:
Online Resource
ISSN:
0217-751X
,
1793-656X
DOI:
10.1142/S0217751X03014228
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2003
SSG:
16,12
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