U(1)(m) modular invariants, N=2 minimal models, and the quantum Hall effect

被引:24
|
作者
Gannon, T [1 ]
机构
[1] MAX PLANCK INST MATH, D-53225 BONN, GERMANY
关键词
quantum Hall effect; N = 2 minimal models;
D O I
10.1016/S0550-3213(97)00032-1
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
The problem of finding all possible effective field theories for the quantum Hall effect is closely related to the problem of classifying all possible modular invariant partition functions for the algebra <(u(1)(+m))over cap>, as was argued recently by Cappelli and Zemba. This latter problem is also a natural one from the perspective of conformal field theory. In this paper we completely solve this problem, expressing the answer in terms of self-dual lattices, or equivalently, rational points on the dual Grassmannian G(m,m)(R)*. We also find all modular invariant partition functions for affine su(2) + u(1)(+m), from which we obtain the classification of all N = 2 superconformal minimal models. The 'A-D-E classification' of these, though often quoted in the literature, turns out to be a very coarse-grained one: e.g. associated with the names E-6, E-7, E-8, respectively, are precisely 20, 30, 24 different partition functions. As a by-product of our analysis, we find that the list of modular invariants for <(su(2))over cap> lengthens surprisingly little when commutation with T - i.e. invariance under tau bar right arrow tau + 1 - is ignored: the other conditions are far more essential. (C) 1997 Elsevier Science B.V.
引用
收藏
页码:659 / 688
页数:30
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