N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
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DOI：
10.1088/1126-6708/2008/10/091
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发表时间：
2008-10-01
影响因子：
5.4
通讯作者：
Maldacena, Juan
中科院分区：
文献类型：
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作者：
Aharony, Ofer;Bergman, Oren;Maldacena, Juan
我们构造了具有显式N=6超共形对称性的规范群U(N)x U(N)和SU(N)x SU(N)的三维Chern-Simons物质理论。利用膜结构，我们认为在k能级的U(N)×U(N)理论描述了N个M2膜探测C-4/Z(K)奇点的能量下限。在大N下，该理论对偶于ADS(4)×S-7/Z(K)上的M-理论。这个理论也有一个‘t Hooft极限(N/k比固定的大N)，它对偶于Ads(4)x CP3上的IIA型弦理论。对于k=1，这个理论被猜想来描述平坦空间中的N个M2膜，尽管我们的构造只显式地实现了8个超对称中的6个。我们给出了这个猜想的一些证据，这类似于d=3规范理论中关于镜像对称性的证据。当规范群是SU(2)x SU(2)时，我们的理论具有额外的对称性，并且变得与Bagger-Lambert理论相同。
We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) x U(N) and SU(N) x SU(N) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U(N) x U(N) theory at level k describes the low energy limit of N M2-branes probing a C-4/Z(k) singularity. At large N the theory is then dual to M-theory on AdS(4) x S-7/Z(k). The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS(4) x CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) x SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.