共形场论中的m-约化为两环面上的Morita等价
The m-reduction in Conformal Field Theory as the Morita equivalence on two-tori
摘要：
研究了非对易二环面上场论的Morita等价性。对于非对易性参数$θ$的有理值（以适当的单位表示），我们证明了阿贝尔非对易场论与普通空间上扭曲场的非阿贝尔理论之间的等价性。我们集中讨论一种特殊的共形场论（CFT），即通过m-约化过程得到的场论（V. Marotta，J.Phys.A26（1993）3481; Mod. Phys. Lett. A13（1998）853; Nucl.Phys.B527（1998）717），并表明Morita等价性在该水平也成立。为了进一步阐明这种对应关系，我们考虑了在Jain填充数ν=m/2pm+1时量子Hall流体物理中的一个应用.
英文摘要：
We study the Morita equivalence for field theories on noncommutative two-tori. For rational values of the noncommutativity parameter $θ$ (in appropriate units) we show the equivalence between an abelian noncommutative field theory and a nonabelian theory of twisted fields on ordinary space. We concentrate on a particular conformal field theory (CFT), the one obtained by means of the m-reduction procedure (V. Marotta, J. Phys. A 26 (1993) 3481; Mod. Phys. Lett. A 13 (1998) 853; Nucl. Phys. B 527 (1998) 717), and show that the Morita equivalence also holds at this level. An application to the physics of a quantum Hall fluid at Jain fillings ν=m/2pm+1 is explicitly considered in order to further elucidate such a correspondence.
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