arXiv 1404.78492014-04hep-thcond-mat.str-el

非超对称双基本Chern-Simons理论中的反常维数

Anomalous Dimensions in Non-Supersymmetric Bifundamental Chern-Simons Theories

V. Gurucharan, Shiroman Prakash

备注：: 16 pages; v5: added corrections
发表信息：: JHEP 1409 (2014) 009
DOI：: 10.1007/JHEP09(2014)009

摘要：

耦合到费米子的非阿贝尔陈-西蒙斯理论提供了一类有趣的非超对称共形不动点\cite{Giombi:2011kc}。这些理论，特别是那些基于双基本物质的理论，是很重要的，因为它们可以提供简单的AdS/CFT对应的非超对称例子。例如，人们很自然地猜想，耦合到马约拉纳费米子变换的$O(N)_{-k}\times O(N)_k$ Chern-Simons理论在双矢量表示中可能是纯爱因斯坦引力的对偶，在“M理论”极限中，$k=1$和$N$都很大。虽然当$k=1$或甚至在强的t Hooft耦合$λ=\frac{N}{k}$时直接研究这样的双基本理论是极其困难的，但是在$U(M)_{k_M} \times U(N)_{k_N}$理论中、在极限$M \ll N$中、在$M/N$展开中计算$λ$中的所有阶的物理量是可能的。为了说明这一点，我们计算的异常尺寸的主要运营商$\barψψ$，一阶$M/N$，所有订单$λ_M=\frac{N}{k_M}$，但与$λ_N=\frac{N}{k_N}=0$。我们还评论可能的玻色化对偶的bifundamental陈-西蒙斯理论。

英文摘要：

Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points \cite{Giombi:2011kc}. These theories, particularly those based on bifundamental matter, are important because they may provide simple non-supersymmetric examples of the AdS/CFT correspondence. For instance, it seems natural to conjecture that $O(N)_{-k}\times O(N)_k$ Chern-Simons theory coupled to Majorana fermions transforming in a bi-vector representation may be dual to pure Einstein gravity with a small negative cosmological constant in the "M-theory" limit where $k=1$ and $N$ is large. While it is extremely difficult to directly study such bifundamental theories when $k=1$ or even at strong 't Hooft coupling $λ=\frac{N}{k}$, it is possible to calculate physical quantities to all orders in $λ$ in a $U(M)_{k_M} \times U(N)_{k_N}$ theory, in the limit $M \ll N$, in an $M/N$ expansion. To illustrate this, we calculate the anomalous dimension of the primary operator $\barψψ$, to first order in $M/N$, to all orders in $λ_M=\frac{N}{k_M}$, but with $λ_N=\frac{N}{k_N}=0$. We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.

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