arXiv 1502.009452015-02hep-th

超对称Chern-Simons物质理论中的非线性算子

On monopole operators in supersymmetric Chern-Simons-matter theories

Ofer Aharony, Prithvi Narayan, Tarun Sharma

备注：: 39 pages. v2: fixed typos

摘要：

本文讨论了三维时空中$U(N_c)$ Chern-Simons物质理论中的算符。我们提到了一个明显的问题，在非超对称理论之间的对偶匹配这样的运营商，并提出了一个可能的解决方案。在具有${\cal N}=2$超对称性的理论中，手征算符的映射也存在类似的明显问题。我们表明，在许多理论中，最低的天真手征的手征的操作者实际上是不是手征的，我们发现最低的手征的操作者，实际上是手征在这些理论。事实证明，这个算子有几种不同的形式，取决于颜色的数量，味道的数量和Chern-Simons水平。由于我们使用超对称指数来寻找最低的手征单极子，因此我们的结果在超对称理论的对偶下是不变的。我们所讨论的理论被认为是经典高自旋引力理论在't~Hooft大$N_c$极限下的对偶。我们认为，这些理论（超对称或不）不应该有经典的解决方案下的高自旋多重态的$U(1)$规范场收费。

英文摘要：

We discuss monopole operators in $U(N_c)$ Chern-Simons-matter theories in three space-time dimensions. We mention an apparent problem in the matching of such operators in dualities between non-supersymmetric theories, and suggest a possible resolution. A similar apparent problem exists in the mapping of chiral monopole operators in theories with ${\cal N}=2$ supersymmetry. We show that in many theories the lowest naive chiral monopole operator is actually not chiral, and we find the lowest monopole operator that is actually chiral in these theories. It turns out that there are several different forms of this operator, depending on the number of colors, the number of flavours, and the Chern-Simons level. Since we use the supersymmetric index to find the lowest chiral monopoles, our results for these monopoles are guaranteed to be invariant under the dualities in supersymmetric theories. The theories we discuss are believed to be dual in the 't~Hooft large $N_c$ limit to classical high-spin gravity theories. We argue that these theories (supersymmetric or not) should not have classical solutions charged under the $U(1)$ gauge field in the high-spin multiplet.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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