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arXiv 0812.1331hep-th
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N=4的Chern-Simons理论及其引力场中的M-膜

N=4 Chern-Simons theories and wrapped M-branes in their gravity duals

Yosuke Imamura, Shuichi Yokoyama

摘要:

研究了一类N=4的Chern-Simons理论及其引力场.在考虑Hanany-Witten效应产生D3-膜的情况下,定义了IIB型膜系统中的分数D3-膜荷群,并证明了它与描述分数M2-膜、M5-膜包裹在3-圈上的荷的对偶几何的3-圈同调一致.部分地建立了分数膜荷与三型势场挠率的关系。我们还讨论了Chern-Simons理论中重子算子与对偶几何中包裹在5-圈上的M5-膜之间的对偶性。算子的简并性和共形维度在重力侧重现。我们还讨论了包裹M2-膜与M2-算子之间的关系。我们考虑的重子算符不是规范不变的。我们认为,规范不变性不能强加给所有的运营商对应的包装M膜在AdS 4/CFT 3的对应。

英文摘要:

We investigate a class of N=4 quiver Chern-Simons theories and their gravity duals. We define the group of fractional D3-brane charges in a type IIB brane setup with taking account of D3-brane creation due to Hanany-Witten effect, and confirm that it agrees with the 3-cycle homology of the dual geometry, which describes the charges of fractional M2-branes, M5-branes wrapped on 3-cycles. The relation between the fractional brane charge and the torsion of the three-form potential field is partially established. We also discuss the duality between baryonic operators in the Chern-Simons theories and M5-branes wrapped on 5-cycles in the dual geometries. The degeneracy and the conformal dimension of the operators are reproduced on the gravity side. We also comment on the relation between wrapped M2-branes and monopole operators. The baryonic operators we consider are not gauge invariant. We argue that the gauge invariance cannot be imposed on all the operators corresponding to wrapped M-branes in AdS4/CFT3 correspondence.

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