扭曲共形场论与Morita等价
Twisted Conformal Field Theories and Morita equivalence
摘要：
森田等价的场论的非交换两环面的非交换参数θ（在适当的单位）的合理值进行了详细分析：同构之间建立一个阿贝尔非交换场论（NCFT）和非阿贝尔理论的扭曲领域的普通空间。我们集中在一个特定的共形场论（CFT），一个通过m-约化过程（V. Marotta，J.Phys.A26（1993）3481; V. Marotta，Mod. Phys. Lett. A 13}（1998）853; V. Marotta，Nucl.Phys.B527（1998）717; V. Marotta，A. Sciarrino，Mod. Phys. Lett. A13（1998）2863），并表明它是NCFT的Morita等价物。最后证明了整个m-约化过程是Morita对偶在平凡空间中的映象。为了进一步阐明这种对应关系，并阐明它在强关联系统物理中的作用，明确讨论了量子霍尔流体在Jain填充nu =m/2pm+1时的物理应用。一个新的图景出现了，它与非对易性和许多身体系统之间的现有关系非常不同（A。P. Polychronakos，arXiv：0706.1095v2）.
英文摘要：
The Morita equivalence for field theories on noncommutative two-tori is analysed in detail for rational values of the noncommutativity parameter theta (in appropriate units): an isomorphism is established between an abelian noncommutative field theory (NCFT) and a non-abelian theory of twisted fields on ordinary space. We focus 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; V. Marotta, Mod. Phys. Lett. A 13} (1998) 853; V. Marotta, Nucl. Phys. B 527 (1998) 717; V. Marotta, A. Sciarrino, Mod. Phys. Lett. A 13 (1998) 2863), and show that it is the Morita equivalent of a NCFT. Finally, the whole m-reduction procedure is shown to be the image in the ordinary space of the Morita duality. An application to the physics of a quantum Hall fluid at Jain fillings nu =m/2pm+1 is explicitly discussed in order to further elucidate such a correspondence and to clarify its role in the physics of strongly correlated systems. A new picture emerges, which is very different from the existing relationships between noncommutativity and many body systems (A. P. Polychronakos, arXiv:0706.1095v2).
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