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arXiv 1208.6085hep-th
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N=5与N=6的对偶性陈-西蒙斯物质理论

Duality between N=5 and N=6 Chern-Simons matter theory

Sangmo Cheon, Dongmin Gang, Chiung Hwang, Satoshi Nagaoka, Jaemo Park

备注：
15 pages; references added
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摘要：

通过计算超共形指数，证明了${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons物质理论和${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$理论之间的对偶性，从而得到了一个合适的$\hat{M},\hat{N}$，它显示出完美的匹配.对于${\cal N}=5$理论，我们表明，超对称性增强到${\cal N}=6$通过明确地构造填充在$SO(6)_R$ $R$ -电流的超对称算子。最后计算出了$O(2N)_{2k} \times USp(2N)_{-k}$的大$N$指数，并证明了它与$AdS_4 \times S^7/D_k$上的重力指数完全匹配，进一步证明了$k=1$的${\cal N}=5$和${\cal N}=6$理论之间的对偶性

英文摘要：

We provide evidences for the duality between ${\cal N}=6$ $U(M)_{4} \times U(N)_{-4}$ Chern-Simons matter theory and ${\cal N}=5$ $O(\hat{M})_{2} \times USp(2\hat{N})_{-1}$ theory for a suitable $\hat{M},\hat{N}$ by working out the superconformal index, which shows perfect matching. For ${\cal N}=5$ theories, we show that supersymmetry is enhanced to ${\cal N}=6$ by explicitly constructing monopole operators filling in $SO(6)_R$ $R$-currents. Finally we work out the large $N$ index of $O(2N)_{2k} \times USp(2N)_{-k}$ and show that it exactly matches with the gravity index on $AdS_4 \times S^7/D_k$, which further provides additional evidence for the duality between the ${\cal N}=5$ and ${\cal N}=6$ theory for $k=1$

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