Solitons on noncommutative torus as elliptic Calogero-Gaudin models, Branes and Laughlin wave functions

	Solitons on noncommutative torus as elliptic Calogero-Gaudin models, Branes and Laughlin wave functions
	Hou, BY; Peng, DT; Shi, KJ; Yue, RH
刊名	INTERNATIONAL JOURNAL OF MODERN PHYSICS A
	2003-06-10
卷号	18 页码:2477-2500
关键词	noncommutative torus elliptic Gaudin model Calogero-Moser model spectral curve branes Quantum Hall effect Laughlin wave function
ISSN号	0217-751X
英文摘要	For the noncommutative torus T, in the case of the noncommutative parameter theta = z/n, we construct the basis of Hilbert space H-n in terms of theta functions of the positions Z(i) of n solitons. The wrapping around the torus generates the algebra A(n), which is the Z(n) x Z(n) Heisenberg group on theta functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of A(n). By acting on H-n we establish the isomorphism of An 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 sun(T) 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 Tcircle times(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 su(n)(T) cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.
WOS关键词	ALGEBRAIC BETHE-ANSATZ ; YANG-MILLS THEORY ; EQUATIONS ; SYSTEMS ; OPERATORS ; CURVES
WOS研究方向	Physics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000183428200003
内容类型	期刊论文
源URL	[http://119.78.100.186/handle/113462/38789]
专题	中国科学院近代物理研究所
通讯作者	Hou, BY
作者单位	NW Univ Xian, Inst Modern Phys, Xian 710069, Peoples R China
推荐引用方式 GB/T 7714	Hou, BY,Peng, DT,Shi, KJ,et al. Solitons on noncommutative torus as elliptic Calogero-Gaudin models, Branes and Laughlin wave functions[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS A,2003,18:2477-2500.
APA	Hou, BY,Peng, DT,Shi, KJ,&Yue, RH.(2003).Solitons on noncommutative torus as elliptic Calogero-Gaudin models, Branes and Laughlin wave functions.INTERNATIONAL JOURNAL OF MODERN PHYSICS A,18,2477-2500.
MLA	Hou, BY,et al."Solitons on noncommutative torus as elliptic Calogero-Gaudin models, Branes and Laughlin wave functions".INTERNATIONAL JOURNAL OF MODERN PHYSICS A 18(2003):2477-2500.