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arXiv 2011.11240hep-th
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类Grassmannian陪集模型与高自旋流

The Grassmannian-like Coset Model and the Higher Spin Currents

Changhyun Ahn

备注：
86 pages;The footnote 2 is added, the section 8 is moved to Appendix H, the section 1 is improved, the redundant explanations are removed and to appear in JHEP
发表信息：
JHEP 03,037 (2021)
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摘要：

在类格拉斯曼陪集模型中，$\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$，Creutzig和Hikida等人已经发现了带电的自旋$2,3$电流和中性的自旋$2,3$电流.作为10年前提出的Gaberdiel-Gopakumar猜想的推广，本文计算了一般$N, M$和$k$的荷电自旋$2$流与自身的算符积展开（OPE），荷电自旋$2$流与荷电自旋$3$流的算符积展开，以及中性自旋$3$流与自身的算符积展开.从第二个OPE中，我们得到了新的带电准主自旋- $4$流，而从第三个OPE中，我们隐式地得到了新的中性主自旋- $4$流。在$AdS_3$高自旋理论的$M \times M$矩阵推广的渐近对称性的背景下，描述了$k$在OPEs结构常数中的无穷大极限。此外，对于固定的$(N,M)=(5,4)$和直到三阶极点的任意$k$，确定了带电自旋$3$电流与其自身之间的OPE.我们还得到了带电自旋$1,2,3$电流和中性自旋$3$电流之间的OPEs。由最后的OPE，我们认识到，对于固定的$(N,M)=(5,4)$，在二阶极中存在上述带电准初级自旋$4$流。我们对复自由费米子的实现作了评述。

英文摘要：

In the Grassmannian-like coset model, $\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$, Creutzig and Hikida have found the charged spin-$2,3$ currents and the neutral spin-$2,3$ currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-$2$ current and itself, the OPE between the charged spin-$2$ current and the charged spin-$3$ current and the OPE between the neutral spin-$3$ current and itself for generic $N, M$ and $k$. From the second OPE, we obtain the new charged quasi primary spin-$4$ current while from the last one, the new neutral primary spin-$4$ current is found implicitly. The infinity limit of $k$ in the structure constants of the OPEs is described in the context of asymptotic symmetry of $M \times M$ matrix generalization of $AdS_3$ higher spin theory. Moreover, the OPE between the charged spin-$3$ current and itself is determined for fixed $(N,M)=(5,4)$ with arbitrary $k$ up to the third order pole. We also obtain the OPEs between charged spin-$1,2,3$ currents and neutral spin-$3$ current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-$4$ current in the second order pole for fixed $(N,M)=(5,4)$. We comment on the complex free fermion realization.

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